diff --git a/inputFiles/compositionalMultiphaseFlow/benchmarks/isothermalLeakyWell/isothermalLeakyWell_base_direct.xml b/inputFiles/compositionalMultiphaseFlow/benchmarks/isothermalLeakyWell/isothermalLeakyWell_base_direct.xml
index 921966dad20..25668102c78 100644
--- a/inputFiles/compositionalMultiphaseFlow/benchmarks/isothermalLeakyWell/isothermalLeakyWell_base_direct.xml
+++ b/inputFiles/compositionalMultiphaseFlow/benchmarks/isothermalLeakyWell/isothermalLeakyWell_base_direct.xml
@@ -47,7 +47,7 @@
       target="/Solvers/compflow"/>
     <PeriodicEvent
       name="solverApplications2"
-      beginTime="1e5"   
+      beginTime="1e5"
       forceDt="1e5"
       target="/Solvers/compflow"/>
     <PeriodicEvent
@@ -72,19 +72,15 @@
   <ElementRegions>
     <CellElementRegion
       name="aquiferBottom"
-      cellBlocks="{ aquiferBottom00, aquiferBottom01, aquiferBottom02,
-                    aquiferBottom10,                  aquiferBottom12,
-                    aquiferBottom20, aquiferBottom21, aquiferBottom22,
-                    aquiferBottom30,                  aquiferBottom32,
-                    aquiferBottom40, aquiferBottom41, aquiferBottom42 }"
+      cellBlocks="{ aquiferBottom00, aquiferBottom10, aquiferBottom20, aquiferBottom30, aquiferBottom40,
+                    aquiferBottom01,                  aquiferBottom21,                  aquiferBottom41,
+                    aquiferBottom02, aquiferBottom12, aquiferBottom22, aquiferBottom32, aquiferBottom42 }"
       materialList="{ fluid, rock, relperm }"/>
     <CellElementRegion
       name="aquiferTop"
-      cellBlocks="{ aquiferTop00, aquiferTop01, aquiferTop02,
-                    aquiferTop10,               aquiferTop12,
-                    aquiferTop20, aquiferTop21, aquiferTop22,
-                    aquiferTop30,               aquiferTop32,
-                    aquiferTop40, aquiferTop41, aquiferTop42 }"
+      cellBlocks="{ aquiferTop00, aquiferTop10, aquiferTop20, aquiferTop30, aquiferTop40,
+                    aquiferTop01,               aquiferTop21,               aquiferTop41,
+		    aquiferTop02, aquiferTop12, aquiferTop22, aquiferTop32, aquiferTop42 }"
       materialList="{ fluid, rock, relperm }"/>
     <CellElementRegion
       name="injectionWell"
@@ -92,16 +88,14 @@
       materialList="{ fluid, rockWell, relperm }"/>
     <CellElementRegion
       name="leakyWell"
-      cellBlocks="{ aquiferTop11, aquitard11, aquiferBottom11 }"
+      cellBlocks="{ aquiferBottom11, aquitard11, aquiferTop11 }"
       materialList="{ fluid, rockWell, relperm }"/>
     <CellElementRegion
       name="barrier"
-      cellBlocks="{ aquitard00, aquitard01, aquitard02,
-                    aquitard10,             aquitard12,
-                    aquitard20, aquitard21, aquitard22,
-                    aquitard30, aquitard31, aquitard32,
-                    aquitard40, aquitard41, aquitard42,
-                    aquiferTop31 }"
+      cellBlocks="{ aquitard00, aquitard10, aquitard20, aquitard30, aquitard40,
+                    aquitard01,             aquitard21, aquitard31, aquitard41,
+                    aquitard02, aquitard12, aquitard22, aquitard32, aquitard42,
+                                                        aquiferTop31 }"
       materialList="{ }"/>
   </ElementRegions>
   <!-- SPHINX_ELEMENT_REGIONS_END -->    
diff --git a/inputFiles/compositionalMultiphaseFlow/benchmarks/isothermalLeakyWell/isothermalLeakyWell_base_iterative.xml b/inputFiles/compositionalMultiphaseFlow/benchmarks/isothermalLeakyWell/isothermalLeakyWell_base_iterative.xml
index dea8dc17e22..a70fd719ee6 100644
--- a/inputFiles/compositionalMultiphaseFlow/benchmarks/isothermalLeakyWell/isothermalLeakyWell_base_iterative.xml
+++ b/inputFiles/compositionalMultiphaseFlow/benchmarks/isothermalLeakyWell/isothermalLeakyWell_base_iterative.xml
@@ -2,7 +2,7 @@
 
 <Problem>
   
-  <!-- SPHINX_SOLVER -->      
+  <!-- SPHINX_SOLVER -->
   <Solvers>
     <CompositionalMultiphaseFVM
       name="compflow"
@@ -60,19 +60,15 @@
   <ElementRegions>
     <CellElementRegion
       name="aquiferBottom"
-      cellBlocks="{ aquiferBottom00, aquiferBottom01, aquiferBottom02,
-                    aquiferBottom10,                  aquiferBottom12,
-                    aquiferBottom20, aquiferBottom21, aquiferBottom22,
-                    aquiferBottom30,                  aquiferBottom32,
-                    aquiferBottom40, aquiferBottom41, aquiferBottom42 }"
+      cellBlocks="{ aquiferBottom00, aquiferBottom10, aquiferBottom20, aquiferBottom30, aquiferBottom40,
+                    aquiferBottom01,                  aquiferBottom21,                  aquiferBottom41,
+                    aquiferBottom02, aquiferBottom12, aquiferBottom22, aquiferBottom32, aquiferBottom42 }"
       materialList="{ fluid, rock, relperm }"/>
     <CellElementRegion
       name="aquiferTop"
-      cellBlocks="{ aquiferTop00, aquiferTop01, aquiferTop02,
-                    aquiferTop10,               aquiferTop12,
-                    aquiferTop20, aquiferTop21, aquiferTop22,
-                    aquiferTop30,               aquiferTop32,
-                    aquiferTop40, aquiferTop41, aquiferTop42 }"
+      cellBlocks="{ aquiferTop00, aquiferTop10, aquiferTop20, aquiferTop30, aquiferTop40,
+                    aquiferTop01,               aquiferTop21,               aquiferTop41,
+                    aquiferTop02, aquiferTop12, aquiferTop22, aquiferTop32, aquiferTop42 }"
       materialList="{ fluid, rock, relperm }"/>
     <CellElementRegion
       name="injectionWell"
@@ -80,16 +76,14 @@
       materialList="{ fluid, rockWell, relperm }"/>
     <CellElementRegion
       name="leakyWell"
-      cellBlocks="{ aquiferTop11, aquitard11, aquiferBottom11 }"
+      cellBlocks="{ aquiferBottom11, aquitard11, aquiferTop11 }"
       materialList="{ fluid, rockWell, relperm }"/>
     <CellElementRegion
       name="barrier"
-      cellBlocks="{ aquitard00, aquitard01, aquitard02,
-                    aquitard10,             aquitard12,
-                    aquitard20, aquitard21, aquitard22,
-                    aquitard30, aquitard31, aquitard32,
-                    aquitard40, aquitard41, aquitard42,
-                    aquiferTop31 }"
+      cellBlocks="{ aquitard00, aquitard10, aquitard20, aquitard30, aquitard40,
+                    aquitard01,             aquitard21, aquitard31, aquitard41,
+                    aquitard02, aquitard12, aquitard22, aquitard32, aquitard42,
+                                                        aquiferTop31 }"
       materialList="{ }"/>
   </ElementRegions>
   <!-- SPHINX_ELEMENT_REGIONS_END -->    
diff --git a/inputFiles/compositionalMultiphaseFlow/benchmarks/isothermalLeakyWell/isothermalLeakyWell_benchmark.xml b/inputFiles/compositionalMultiphaseFlow/benchmarks/isothermalLeakyWell/isothermalLeakyWell_benchmark.xml
index cd134e9e2f1..3edd2f02657 100644
--- a/inputFiles/compositionalMultiphaseFlow/benchmarks/isothermalLeakyWell/isothermalLeakyWell_benchmark.xml
+++ b/inputFiles/compositionalMultiphaseFlow/benchmarks/isothermalLeakyWell/isothermalLeakyWell_benchmark.xml
@@ -18,21 +18,15 @@
       nx="{ 50, 1, 20, 1, 40 }"
       ny="{ 50, 1, 50 }"
       nz="{ 20, 30, 10 }"
-      cellBlockNames="{ aquiferBottom00, aquitard00, aquiferTop00,
-  		        aquiferBottom01, aquitard01, aquiferTop01,
-		        aquiferBottom02, aquitard02, aquiferTop02,
- 		        aquiferBottom10, aquitard10, aquiferTop10,
-  		        aquiferBottom11, aquitard11, aquiferTop11,
-		        aquiferBottom12, aquitard12, aquiferTop12,
-		        aquiferBottom20, aquitard20, aquiferTop20,
-  		        aquiferBottom21, aquitard21, aquiferTop21,
-		        aquiferBottom22, aquitard22, aquiferTop22,
-		        aquiferBottom30, aquitard30, aquiferTop30,
-		        aquiferBottom31, aquitard31, aquiferTop31,
-			aquiferBottom32, aquitard32, aquiferTop32,
-			aquiferBottom40, aquitard40, aquiferTop40,
-		        aquiferBottom41, aquitard41, aquiferTop41,
-			aquiferBottom42, aquitard42, aquiferTop42 }"/>
+      cellBlockNames="{ aquiferBottom00, aquiferBottom10, aquiferBottom20, aquiferBottom30, aquiferBottom40, 
+                        aquiferBottom01, aquiferBottom11, aquiferBottom21, aquiferBottom31, aquiferBottom41, 
+                        aquiferBottom02, aquiferBottom12, aquiferBottom22, aquiferBottom32, aquiferBottom42, 
+                             aquitard00,      aquitard10,      aquitard20,      aquitard30,      aquitard40, 
+                             aquitard01,      aquitard11,      aquitard21,      aquitard31,      aquitard41, 
+                             aquitard02,      aquitard12,      aquitard22,      aquitard32,      aquitard42, 
+                           aquiferTop00,    aquiferTop10,    aquiferTop20,    aquiferTop30,    aquiferTop40,
+                           aquiferTop01,    aquiferTop11,    aquiferTop21,    aquiferTop31,    aquiferTop41,
+                           aquiferTop02,    aquiferTop12,    aquiferTop22,    aquiferTop32,    aquiferTop42 }"/>
   </Mesh>
   <!-- SPHINX_MESH_END -->  
   
diff --git a/inputFiles/compositionalMultiphaseFlow/benchmarks/isothermalLeakyWell/isothermalLeakyWell_smoke_3d.xml b/inputFiles/compositionalMultiphaseFlow/benchmarks/isothermalLeakyWell/isothermalLeakyWell_smoke_3d.xml
index 775890d368f..69362de80c4 100644
--- a/inputFiles/compositionalMultiphaseFlow/benchmarks/isothermalLeakyWell/isothermalLeakyWell_smoke_3d.xml
+++ b/inputFiles/compositionalMultiphaseFlow/benchmarks/isothermalLeakyWell/isothermalLeakyWell_smoke_3d.xml
@@ -18,21 +18,15 @@
       nx="{ 5, 1, 2, 1, 4 }"
       ny="{ 5, 1, 5 }"
       nz="{ 5, 30, 5 }"
-      cellBlockNames="{ aquiferBottom00, aquitard00, aquiferTop00,
-                        aquiferBottom01, aquitard01, aquiferTop01,
-                        aquiferBottom02, aquitard02, aquiferTop02,
-                        aquiferBottom10, aquitard10, aquiferTop10,
-                        aquiferBottom11, aquitard11, aquiferTop11,
-                        aquiferBottom12, aquitard12, aquiferTop12,
-                        aquiferBottom20, aquitard20, aquiferTop20,
-                        aquiferBottom21, aquitard21, aquiferTop21,
-                        aquiferBottom22, aquitard22, aquiferTop22,
-                        aquiferBottom30, aquitard30, aquiferTop30,
-                        aquiferBottom31, aquitard31, aquiferTop31,
-                        aquiferBottom32, aquitard32, aquiferTop32,
-                        aquiferBottom40, aquitard40, aquiferTop40,
-                        aquiferBottom41, aquitard41, aquiferTop41,
-                        aquiferBottom42, aquitard42, aquiferTop42 }"/>
+      cellBlockNames="{ aquiferBottom00, aquiferBottom10, aquiferBottom20, aquiferBottom30, aquiferBottom40, 
+                        aquiferBottom01, aquiferBottom11, aquiferBottom21, aquiferBottom31, aquiferBottom41, 
+                        aquiferBottom02, aquiferBottom12, aquiferBottom22, aquiferBottom32, aquiferBottom42, 
+                             aquitard00,      aquitard10,      aquitard20,      aquitard30,      aquitard40, 
+                             aquitard01,      aquitard11,      aquitard21,      aquitard31,      aquitard41, 
+                             aquitard02,      aquitard12,      aquitard22,      aquitard32,      aquitard42, 
+                           aquiferTop00,    aquiferTop10,    aquiferTop20,    aquiferTop30,    aquiferTop40,
+                           aquiferTop01,    aquiferTop11,    aquiferTop21,    aquiferTop31,    aquiferTop41,
+			   aquiferTop02,    aquiferTop12,    aquiferTop22,    aquiferTop32,    aquiferTop42 }"/>
   </Mesh>
   <!-- SPHINX_MESH_END -->  
   
diff --git a/inputFiles/compositionalMultiphaseFlow/benchmarks/thermalLeakyWell/thermalLeakyWell_base_direct.xml b/inputFiles/compositionalMultiphaseFlow/benchmarks/thermalLeakyWell/thermalLeakyWell_base_direct.xml
index 9680e6ef85f..961d7c6d00d 100644
--- a/inputFiles/compositionalMultiphaseFlow/benchmarks/thermalLeakyWell/thermalLeakyWell_base_direct.xml
+++ b/inputFiles/compositionalMultiphaseFlow/benchmarks/thermalLeakyWell/thermalLeakyWell_base_direct.xml
@@ -73,19 +73,15 @@
   <ElementRegions>
     <CellElementRegion
       name="aquiferBottom"
-      cellBlocks="{ aquiferBottom00, aquiferBottom01, aquiferBottom02,
-		    aquiferBottom10,                  aquiferBottom12,
-		    aquiferBottom20, aquiferBottom21, aquiferBottom22,
-		    aquiferBottom30,                  aquiferBottom32,
-		    aquiferBottom40, aquiferBottom41, aquiferBottom42 }"
+      cellBlocks="{ aquiferBottom00, aquiferBottom10, aquiferBottom20, aquiferBottom30, aquiferBottom40,
+                    aquiferBottom01,                  aquiferBottom21,                  aquiferBottom41,
+		                aquiferBottom02, aquiferBottom12, aquiferBottom22, aquiferBottom32, aquiferBottom42 }"
       materialList="{ fluid, rock, relperm, cappres }"/>
     <CellElementRegion
       name="aquiferTop"
-      cellBlocks="{ aquiferTop00, aquiferTop01, aquiferTop02,
-		    aquiferTop10,               aquiferTop12,
-		    aquiferTop20, aquiferTop21, aquiferTop22,
-		    aquiferTop30,               aquiferTop32,
-		    aquiferTop40, aquiferTop41, aquiferTop42 }"
+      cellBlocks="{ aquiferTop00, aquiferTop10, aquiferTop20, aquiferTop30, aquiferTop40,
+                    aquiferTop01,               aquiferTop21,               aquiferTop41,
+		                aquiferTop02, aquiferTop12, aquiferTop22, aquiferTop32, aquiferTop42 }"
       materialList="{ fluid, rock, relperm, cappres }"/>
     <CellElementRegion
       name="injectionWell"
@@ -93,16 +89,14 @@
       materialList="{ fluid, rockWell, relperm, cappres }"/>
     <CellElementRegion
       name="leakyWell"
-      cellBlocks="{ aquiferTop11, aquitard11, aquiferBottom11 }"
+      cellBlocks="{ aquiferBottom11, aquitard11, aquiferTop11 }"
       materialList="{ fluid, rockWell, relperm, cappres }"/>
     <CellElementRegion
       name="barrier"
-      cellBlocks="{ aquitard00, aquitard01, aquitard02,
-                    aquitard10,             aquitard12,
-                    aquitard20, aquitard21, aquitard22,
-                    aquitard30, aquitard31, aquitard32,
-                    aquitard40, aquitard41, aquitard42,
-                    aquiferTop31 }"
+      cellBlocks="{ aquitard00, aquitard10, aquitard20, aquitard30, aquitard40,
+                    aquitard01,             aquitard21, aquitard31, aquitard41,
+                    aquitard02, aquitard12, aquitard22, aquitard32, aquitard42,
+                                                        aquiferTop31 }"
       materialList="{ }"/>
   </ElementRegions>
   <!-- SPHINX_ELEMENT_REGIONS_END -->    
diff --git a/inputFiles/compositionalMultiphaseFlow/benchmarks/thermalLeakyWell/thermalLeakyWell_base_iterative.xml b/inputFiles/compositionalMultiphaseFlow/benchmarks/thermalLeakyWell/thermalLeakyWell_base_iterative.xml
index 91ec5e502d4..985cec900ae 100644
--- a/inputFiles/compositionalMultiphaseFlow/benchmarks/thermalLeakyWell/thermalLeakyWell_base_iterative.xml
+++ b/inputFiles/compositionalMultiphaseFlow/benchmarks/thermalLeakyWell/thermalLeakyWell_base_iterative.xml
@@ -61,19 +61,15 @@
   <ElementRegions>
     <CellElementRegion
       name="aquiferBottom"
-      cellBlocks="{ aquiferBottom00, aquiferBottom01, aquiferBottom02,
-		    aquiferBottom10,                  aquiferBottom12,
-		    aquiferBottom20, aquiferBottom21, aquiferBottom22,
-		    aquiferBottom30,                  aquiferBottom32,
-		    aquiferBottom40, aquiferBottom41, aquiferBottom42 }"
+      cellBlocks="{ aquiferBottom00, aquiferBottom10, aquiferBottom20, aquiferBottom30, aquiferBottom40,
+                    aquiferBottom01,                  aquiferBottom21,                  aquiferBottom41,
+		                aquiferBottom02, aquiferBottom12, aquiferBottom22, aquiferBottom32, aquiferBottom42 }"
       materialList="{ fluid, rock, relperm, cappres }"/>
     <CellElementRegion
       name="aquiferTop"
-      cellBlocks="{ aquiferTop00, aquiferTop01, aquiferTop02,
-		    aquiferTop10,               aquiferTop12,
-		    aquiferTop20, aquiferTop21, aquiferTop22,
-		    aquiferTop30,               aquiferTop32,
-		    aquiferTop40, aquiferTop41, aquiferTop42 }"
+      cellBlocks="{ aquiferTop00, aquiferTop10, aquiferTop20, aquiferTop30, aquiferTop40,
+                    aquiferTop01,               aquiferTop21,               aquiferTop41,
+		                aquiferTop02, aquiferTop12, aquiferTop22, aquiferTop32, aquiferTop42 }"
       materialList="{ fluid, rock, relperm, cappres }"/>
     <CellElementRegion
       name="injectionWell"
@@ -81,16 +77,14 @@
       materialList="{ fluid, rockWell, relperm, cappres }"/>
     <CellElementRegion
       name="leakyWell"
-      cellBlocks="{ aquiferTop11, aquitard11, aquiferBottom11 }"
+      cellBlocks="{ aquiferBottom11, aquitard11, aquiferTop11 }"
       materialList="{ fluid, rockWell, relperm, cappres }"/>
     <CellElementRegion
       name="barrier"
-      cellBlocks="{ aquitard00, aquitard01, aquitard02,
-                    aquitard10,             aquitard12,
-                    aquitard20, aquitard21, aquitard22,
-                    aquitard30, aquitard31, aquitard32,
-                    aquitard40, aquitard41, aquitard42,
-                    aquiferTop31 }"
+      cellBlocks="{ aquitard00, aquitard10, aquitard20, aquitard30, aquitard40,
+                    aquitard01,             aquitard21, aquitard31, aquitard41,
+                    aquitard02, aquitard12, aquitard22, aquitard32, aquitard42,
+                                                        aquiferTop31 }"
       materialList="{ }"/>
   </ElementRegions>
   <!-- SPHINX_ELEMENT_REGIONS_END -->    
diff --git a/inputFiles/compositionalMultiphaseFlow/benchmarks/thermalLeakyWell/thermalLeakyWell_benchmark.xml b/inputFiles/compositionalMultiphaseFlow/benchmarks/thermalLeakyWell/thermalLeakyWell_benchmark.xml
index 7cd5d9467cd..45e0669af83 100644
--- a/inputFiles/compositionalMultiphaseFlow/benchmarks/thermalLeakyWell/thermalLeakyWell_benchmark.xml
+++ b/inputFiles/compositionalMultiphaseFlow/benchmarks/thermalLeakyWell/thermalLeakyWell_benchmark.xml
@@ -18,21 +18,15 @@
       nx="{ 50, 1, 20, 1, 40 }"
       ny="{ 50, 1, 50 }"
       nz="{ 20, 30, 10 }"
-      cellBlockNames="{ aquiferBottom00, aquitard00, aquiferTop00,
-  		        aquiferBottom01, aquitard01, aquiferTop01,
-		        aquiferBottom02, aquitard02, aquiferTop02,
- 		        aquiferBottom10, aquitard10, aquiferTop10,
-  		        aquiferBottom11, aquitard11, aquiferTop11,
-		        aquiferBottom12, aquitard12, aquiferTop12,
-		        aquiferBottom20, aquitard20, aquiferTop20,
-  		        aquiferBottom21, aquitard21, aquiferTop21,
-		        aquiferBottom22, aquitard22, aquiferTop22,
-		        aquiferBottom30, aquitard30, aquiferTop30,
-		        aquiferBottom31, aquitard31, aquiferTop31,
-			aquiferBottom32, aquitard32, aquiferTop32,
-			aquiferBottom40, aquitard40, aquiferTop40,
-		        aquiferBottom41, aquitard41, aquiferTop41,
-			aquiferBottom42, aquitard42, aquiferTop42 }"/>
+      cellBlockNames="{ aquiferBottom00, aquiferBottom10, aquiferBottom20, aquiferBottom30, aquiferBottom40, 
+                        aquiferBottom01, aquiferBottom11, aquiferBottom21, aquiferBottom31, aquiferBottom41, 
+                        aquiferBottom02, aquiferBottom12, aquiferBottom22, aquiferBottom32, aquiferBottom42, 
+                             aquitard00,      aquitard10,      aquitard20,      aquitard30,      aquitard40, 
+                             aquitard01,      aquitard11,      aquitard21,      aquitard31,      aquitard41, 
+                             aquitard02,      aquitard12,      aquitard22,      aquitard32,      aquitard42, 
+                           aquiferTop00,    aquiferTop10,    aquiferTop20,    aquiferTop30,    aquiferTop40,
+                           aquiferTop01,    aquiferTop11,    aquiferTop21,    aquiferTop31,    aquiferTop41,
+			                     aquiferTop02,    aquiferTop12,    aquiferTop22,    aquiferTop32,    aquiferTop42 }"/>
   </Mesh>
   <!-- SPHINX_MESH_END -->  
   
diff --git a/inputFiles/compositionalMultiphaseFlow/benchmarks/thermalLeakyWell/thermalLeakyWell_smoke_3d.xml b/inputFiles/compositionalMultiphaseFlow/benchmarks/thermalLeakyWell/thermalLeakyWell_smoke_3d.xml
index ac2e8ae02d5..3aabd020d74 100644
--- a/inputFiles/compositionalMultiphaseFlow/benchmarks/thermalLeakyWell/thermalLeakyWell_smoke_3d.xml
+++ b/inputFiles/compositionalMultiphaseFlow/benchmarks/thermalLeakyWell/thermalLeakyWell_smoke_3d.xml
@@ -18,21 +18,15 @@
       nx="{ 5, 1, 2, 1, 4 }"
       ny="{ 5, 1, 5 }"
       nz="{ 5, 30, 5 }"
-      cellBlockNames="{ aquiferBottom00, aquitard00, aquiferTop00,
-  		        aquiferBottom01, aquitard01, aquiferTop01,
-		        aquiferBottom02, aquitard02, aquiferTop02,
- 		        aquiferBottom10, aquitard10, aquiferTop10,
-  		        aquiferBottom11, aquitard11, aquiferTop11,
-		        aquiferBottom12, aquitard12, aquiferTop12,
-		        aquiferBottom20, aquitard20, aquiferTop20,
-  		        aquiferBottom21, aquitard21, aquiferTop21,
-		        aquiferBottom22, aquitard22, aquiferTop22,
-		        aquiferBottom30, aquitard30, aquiferTop30,
-		        aquiferBottom31, aquitard31, aquiferTop31,
-			aquiferBottom32, aquitard32, aquiferTop32,
-			aquiferBottom40, aquitard40, aquiferTop40,
-		        aquiferBottom41, aquitard41, aquiferTop41,
-			aquiferBottom42, aquitard42, aquiferTop42 }"/>
+      cellBlockNames="{ aquiferBottom00, aquiferBottom10, aquiferBottom20, aquiferBottom30, aquiferBottom40, 
+                        aquiferBottom01, aquiferBottom11, aquiferBottom21, aquiferBottom31, aquiferBottom41, 
+                        aquiferBottom02, aquiferBottom12, aquiferBottom22, aquiferBottom32, aquiferBottom42, 
+                             aquitard00,      aquitard10,      aquitard20,      aquitard30,      aquitard40, 
+                             aquitard01,      aquitard11,      aquitard21,      aquitard31,      aquitard41, 
+                             aquitard02,      aquitard12,      aquitard22,      aquitard32,      aquitard42, 
+                           aquiferTop00,    aquiferTop10,    aquiferTop20,    aquiferTop30,    aquiferTop40,
+                           aquiferTop01,    aquiferTop11,    aquiferTop21,    aquiferTop31,    aquiferTop41,
+			                     aquiferTop02,    aquiferTop12,    aquiferTop22,    aquiferTop32,    aquiferTop42 }"/>
   </Mesh>
   <!-- SPHINX_MESH_END -->  
   
diff --git a/inputFiles/compositionalMultiphaseFlow/deadoil_2ph_staircase_gravity_segregation_3d.xml b/inputFiles/compositionalMultiphaseFlow/deadoil_2ph_staircase_gravity_segregation_3d.xml
index 23af6f08231..0d9e9853828 100644
--- a/inputFiles/compositionalMultiphaseFlow/deadoil_2ph_staircase_gravity_segregation_3d.xml
+++ b/inputFiles/compositionalMultiphaseFlow/deadoil_2ph_staircase_gravity_segregation_3d.xml
@@ -30,7 +30,10 @@
       nx="{ 5, 5 }"
       ny="{ 5, 5 }"
       nz="{ 3, 3, 3, 3 }"
-      cellBlockNames="{ b00, b01, b02, b03, b04, b05, b06, b07, b08, b09, b10, b11, b12, b13, b14, b15 }"/>
+      cellBlockNames="{ cb-0_0_0, cb-1_0_0, cb-0_1_0, cb-1_1_0,
+                        cb-0_0_1, cb-1_0_1, cb-0_1_1, cb-1_1_1,
+                        cb-0_0_2, cb-1_0_2, cb-0_1_2, cb-1_1_2,
+                        cb-0_0_3, cb-1_0_3, cb-0_1_3, cb-1_1_3 }"/>
   </Mesh>
 
   <Geometry>
@@ -71,12 +74,12 @@
   <ElementRegions>
     <CellElementRegion
       name="Channel"
-      cellBlocks="{ b08, b00, b01, b05, b06, b14, b15, b11 }"
+      cellBlocks="{ cb-1_0_0, cb-0_0_0, cb-0_0_1, cb-0_1_1, cb-0_1_2, cb-1_1_2, cb-1_1_3, cb-1_0_3 }"
       materialList="{ fluid, rock, relperm }"/>
 
     <CellElementRegion
       name="Barrier"
-      cellBlocks="{ b04, b12, b13, b09, b10, b02, b03, b07 }"
+      cellBlocks="{ cb-0_1_0, cb-1_1_0, cb-1_1_1, cb-1_0_1, cb-1_0_2, cb-0_0_2, cb-0_0_3, cb-0_1_3 }"
       materialList="{ }"/>
   </ElementRegions>
 
diff --git a/inputFiles/compositionalMultiphaseFlow/deadoil_3ph_staircase_3d.xml b/inputFiles/compositionalMultiphaseFlow/deadoil_3ph_staircase_3d.xml
index 2b90105cff6..fc452b3d6d1 100644
--- a/inputFiles/compositionalMultiphaseFlow/deadoil_3ph_staircase_3d.xml
+++ b/inputFiles/compositionalMultiphaseFlow/deadoil_3ph_staircase_3d.xml
@@ -31,7 +31,10 @@
       nx="{ 5, 5 }"
       ny="{ 5, 5 }"
       nz="{ 3, 3, 3, 3 }"
-      cellBlockNames="{ b00, b01, b02, b03, b04, b05, b06, b07, b08, b09, b10, b11, b12, b13, b14, b15 }"/>
+      cellBlockNames="{ cb-0_0_0, cb-1_0_0, cb-0_1_0, cb-1_1_0,
+                        cb-0_0_1, cb-1_0_1, cb-0_1_1, cb-1_1_1,
+                        cb-0_0_2, cb-1_0_2, cb-0_1_2, cb-1_1_2,
+                        cb-0_0_3, cb-1_0_3, cb-0_1_3, cb-1_1_3 }"/>
   </Mesh>
 
   <!-- END_SPHINX_INCLUDE_MESH_BLOCK -->
@@ -92,12 +95,12 @@
   <ElementRegions>
     <CellElementRegion
       name="Channel"
-      cellBlocks="{ b08, b00, b01, b05, b06, b14, b15, b11 }"
+      cellBlocks="{ cb-1_0_0, cb-0_0_0, cb-0_0_1, cb-0_1_1, cb-0_1_2, cb-1_1_2, cb-1_1_3, cb-1_0_3 }"
       materialList="{ fluid, rock, relperm }"/>
 
     <CellElementRegion
       name="Barrier"
-      cellBlocks="{ b04, b12, b13, b09, b10, b02, b03, b07 }"
+      cellBlocks="{ cb-0_1_0, cb-1_1_0, cb-1_1_1, cb-1_0_1, cb-1_0_2, cb-0_0_2, cb-0_0_3, cb-0_1_3 }"
       materialList="{ }"/>
   </ElementRegions>
 
diff --git a/inputFiles/compositionalMultiphaseFlow/deadoil_3ph_staircase_hybrid_3d.xml b/inputFiles/compositionalMultiphaseFlow/deadoil_3ph_staircase_hybrid_3d.xml
index e4daec34867..4fe769a93b1 100644
--- a/inputFiles/compositionalMultiphaseFlow/deadoil_3ph_staircase_hybrid_3d.xml
+++ b/inputFiles/compositionalMultiphaseFlow/deadoil_3ph_staircase_hybrid_3d.xml
@@ -29,7 +29,10 @@
       nx="{ 5, 5 }"
       ny="{ 5, 5 }"
       nz="{ 3, 3, 3, 3 }"
-      cellBlockNames="{ b00, b01, b02, b03, b04, b05, b06, b07, b08, b09, b10, b11, b12, b13, b14, b15 }"/>
+      cellBlockNames="{ cb-0_0_0, cb-1_0_0, cb-0_1_0, cb-1_1_0,
+                        cb-0_0_1, cb-1_0_1, cb-0_1_1, cb-1_1_1,
+                        cb-0_0_2, cb-1_0_2, cb-0_1_2, cb-1_1_2,
+                        cb-0_0_3, cb-1_0_3, cb-0_1_3, cb-1_1_3 }"/>
   </Mesh>
 
   <Geometry>
@@ -81,12 +84,12 @@
     <CellElementRegion
       name="Channel"
       meshBody="mesh"
-      cellBlocks="{ b08, b00, b01, b05, b06, b14, b15, b11 }"
+      cellBlocks="{ cb-1_0_0, cb-0_0_0, cb-0_0_1, cb-0_1_1, cb-0_1_2, cb-1_1_2, cb-1_1_3, cb-1_0_3 }"
       materialList="{ fluid, rock, relperm }"/>
 
     <CellElementRegion
       name="Barrier"
-      cellBlocks="{ b04, b12, b13, b09, b10, b02, b03, b07 }"
+      cellBlocks="{ cb-0_1_0, cb-1_1_0, cb-1_1_1, cb-1_0_1, cb-1_0_2, cb-0_0_2, cb-0_0_3, cb-0_1_3 }"
       materialList="{ }"/>
   </ElementRegions>
 
diff --git a/inputFiles/compositionalMultiphaseFlow/deadoil_3ph_staircase_obl_3d.xml b/inputFiles/compositionalMultiphaseFlow/deadoil_3ph_staircase_obl_3d.xml
index 2be6da038ed..f9722261b2b 100644
--- a/inputFiles/compositionalMultiphaseFlow/deadoil_3ph_staircase_obl_3d.xml
+++ b/inputFiles/compositionalMultiphaseFlow/deadoil_3ph_staircase_obl_3d.xml
@@ -34,7 +34,10 @@
       nx="{ 5, 5 }"
       ny="{ 5, 5 }"
       nz="{ 3, 3, 3, 3 }"
-      cellBlockNames="{ b00, b01, b02, b03, b04, b05, b06, b07, b08, b09, b10, b11, b12, b13, b14, b15 }"/>
+      cellBlockNames="{ cb-0_0_0, cb-1_0_0, cb-0_1_0, cb-1_1_0,
+                        cb-0_0_1, cb-1_0_1, cb-0_1_1, cb-1_1_1,
+                        cb-0_0_2, cb-1_0_2, cb-0_1_2, cb-1_1_2,
+                        cb-0_0_3, cb-1_0_3, cb-0_1_3, cb-1_1_3 }"/>
   </Mesh>
 
   <!-- END_SPHINX_INCLUDE_MESH_BLOCK -->
@@ -91,12 +94,12 @@
   <ElementRegions>
     <CellElementRegion
       name="Channel"
-      cellBlocks="{ b08, b00, b01, b05, b06, b14, b15, b11 }"
+      cellBlocks="{ cb-1_0_0, cb-0_0_0, cb-0_0_1, cb-0_1_1, cb-0_1_2, cb-1_1_2, cb-1_1_3, cb-1_0_3 }"
       materialList="{ rock }"/>
 
     <CellElementRegion
       name="Barrier"
-      cellBlocks="{ b04, b12, b13, b09, b10, b02, b03, b07 }"
+      cellBlocks="{ cb-0_1_0, cb-1_1_0, cb-1_1_1, cb-1_0_1, cb-1_0_2, cb-0_0_2, cb-0_0_3, cb-0_1_3 }"
       materialList="{ }"/>
   </ElementRegions>
 
diff --git a/inputFiles/compositionalMultiphaseWell/staircase_co2_wells_3d.xml b/inputFiles/compositionalMultiphaseWell/staircase_co2_wells_3d.xml
index 2c66c759f13..93f9b1469eb 100644
--- a/inputFiles/compositionalMultiphaseWell/staircase_co2_wells_3d.xml
+++ b/inputFiles/compositionalMultiphaseWell/staircase_co2_wells_3d.xml
@@ -65,7 +65,10 @@
       nx="{ 5, 5 }"
       ny="{ 5, 5 }"
       nz="{ 3, 3, 3, 3 }"
-      cellBlockNames="{ b00, b01, b02, b03, b04, b05, b06, b07, b08, b09, b10, b11, b12, b13, b14, b15 }">
+      cellBlockNames="{ cb-0_0_0, cb-1_0_0, cb-0_1_0, cb-1_1_0,
+                        cb-0_0_1, cb-1_0_1, cb-0_1_1, cb-1_1_1,
+                        cb-0_0_2, cb-1_0_2, cb-0_1_2, cb-1_1_2,
+                        cb-0_0_3, cb-1_0_3, cb-0_1_3, cb-1_1_3 }">
 
       <InternalWell
         name="well_producer1"
@@ -120,12 +123,12 @@
   <ElementRegions>
     <CellElementRegion
       name="Channel"
-      cellBlocks="{ b08, b00, b01, b05, b06, b14, b15, b11 }"
+      cellBlocks="{ cb-1_0_0, cb-0_0_0, cb-0_0_1, cb-0_1_1, cb-0_1_2, cb-1_1_2, cb-1_1_3, cb-1_0_3 }"
       materialList="{ fluid1, rock, relperm, cappres, diffusion }"/>
 
     <CellElementRegion
       name="Barrier"
-      cellBlocks="{ b04, b12, b13, b09, b10, b02, b03, b07 }"
+      cellBlocks="{ cb-0_1_0, cb-1_1_0, cb-1_1_1, cb-1_0_1, cb-1_0_2, cb-0_0_2, cb-0_0_3, cb-0_1_3 }"
       materialList="{ }"/>
 
     <WellElementRegion
diff --git a/inputFiles/poromechanics/PoroElastic_staircase_co2_3d_base.xml b/inputFiles/poromechanics/PoroElastic_staircase_co2_3d_base.xml
index 53ca032ac5f..14f540a6a30 100755
--- a/inputFiles/poromechanics/PoroElastic_staircase_co2_3d_base.xml
+++ b/inputFiles/poromechanics/PoroElastic_staircase_co2_3d_base.xml
@@ -12,7 +12,10 @@
       nx="{ 3, 3 }"
       ny="{ 3, 3 }"
       nz="{ 2, 2, 2, 2 }"
-      cellBlockNames="{ b00, b01, b02, b03, b04, b05, b06, b07, b08, b09, b10, b11, b12, b13, b14, b15 }">
+      cellBlockNames="{ cb-0_0_0, cb-1_0_0, cb-0_1_0, cb-1_1_0,
+                        cb-0_0_1, cb-1_0_1, cb-0_1_1, cb-1_1_1,
+                        cb-0_0_2, cb-1_0_2, cb-0_1_2, cb-1_1_2,
+                        cb-0_0_3, cb-1_0_3, cb-0_1_3, cb-1_1_3 }">
 
       <InternalWell
         name="well_producer1"
@@ -66,11 +69,11 @@
   <ElementRegions>
     <CellElementRegion
       name="channel"
-      cellBlocks="{ b08, b00, b01, b05, b06, b14, b15, b11 }"
+      cellBlocks="{ cb-1_0_0, cb-0_0_0, cb-0_0_1, cb-0_1_1, cb-0_1_2, cb-1_1_2, cb-1_1_3, cb-1_0_3 }"
       materialList="{ fluid, porousRockChannel, relperm }"/>
     <CellElementRegion
       name="barrier"
-      cellBlocks="{ b04, b12, b13, b09, b10, b02, b03, b07 }"
+      cellBlocks="{ cb-0_1_0, cb-1_1_0, cb-1_1_1, cb-1_0_1, cb-1_0_2, cb-0_0_2, cb-0_0_3, cb-0_1_3 }"
       materialList="{ fluid, porousRockBarrier, relperm }"/>
     <WellElementRegion
       name="wellRegion1"
diff --git a/inputFiles/poromechanics/PoroElastic_staircase_singlephase_3d_base.xml b/inputFiles/poromechanics/PoroElastic_staircase_singlephase_3d_base.xml
index 5a69dfa2842..bea4a79c816 100755
--- a/inputFiles/poromechanics/PoroElastic_staircase_singlephase_3d_base.xml
+++ b/inputFiles/poromechanics/PoroElastic_staircase_singlephase_3d_base.xml
@@ -12,7 +12,10 @@
       nx="{ 3, 3 }"
       ny="{ 3, 3 }"
       nz="{ 2, 2, 2, 2 }"
-      cellBlockNames="{ b00, b01, b02, b03, b04, b05, b06, b07, b08, b09, b10, b11, b12, b13, b14, b15 }">
+      cellBlockNames="{ cb-0_0_0, cb-1_0_0, cb-0_1_0, cb-1_1_0,
+                        cb-0_0_1, cb-1_0_1, cb-0_1_1, cb-1_1_1,
+                        cb-0_0_2, cb-1_0_2, cb-0_1_2, cb-1_1_2,
+                        cb-0_0_3, cb-1_0_3, cb-0_1_3, cb-1_1_3 }">
 
       <InternalWell
         name="well_producer1"
@@ -66,11 +69,11 @@
   <ElementRegions>
     <CellElementRegion
       name="channel"
-      cellBlocks="{ b08, b00, b01, b05, b06, b14, b15, b11 }"
+      cellBlocks="{ cb-1_0_0, cb-0_0_0, cb-0_0_1, cb-0_1_1, cb-0_1_2, cb-1_1_2, cb-1_1_3, cb-1_0_3 }"
       materialList="{ fluid, porousRockChannel }"/>
     <CellElementRegion
       name="barrier"
-      cellBlocks="{ b04, b12, b13, b09, b10, b02, b03, b07 }"
+      cellBlocks="{ cb-0_1_0, cb-1_1_0, cb-1_1_1, cb-1_0_1, cb-1_0_2, cb-0_0_2, cb-0_0_3, cb-0_1_3 }"
       materialList="{ fluid, porousRockBarrier }"/>
     <WellElementRegion
       name="wellRegion1"
diff --git a/inputFiles/poromechanics/nonlinearAcceleration/validationCase/poroelasticCoupling_validation.ats b/inputFiles/poromechanics/nonlinearAcceleration/validationCase/poroelasticCoupling_validation.ats
index ae39bd6c1d7..1ffd4767566 100644
--- a/inputFiles/poromechanics/nonlinearAcceleration/validationCase/poroelasticCoupling_validation.ats
+++ b/inputFiles/poromechanics/nonlinearAcceleration/validationCase/poroelasticCoupling_validation.ats
@@ -77,7 +77,7 @@ def _build_NonlinearAccelerationValidation_cases():
     description = Description("Nonlinear acceleration validation problem ",
                               "auto", "Sohail Waziri", True)
     restartcheck_params = {"atol": 1.0e-4, "rtol": 2.0e-6}
-    return _build_poro_elastic_coupling_case("validationCase.xml", (3, 6),
+    return _build_poro_elastic_coupling_case("validationCase.xml", (1, 2),
                                              ((1, 1, 1), ), description,
                                              restartcheck_params)
 
diff --git a/inputFiles/poromechanics/nonlinearAcceleration/validationCase/validationCase.xml b/inputFiles/poromechanics/nonlinearAcceleration/validationCase/validationCase.xml
index af9a6c20b5c..e307a69edcf 100755
--- a/inputFiles/poromechanics/nonlinearAcceleration/validationCase/validationCase.xml
+++ b/inputFiles/poromechanics/nonlinearAcceleration/validationCase/validationCase.xml
@@ -16,12 +16,6 @@
         lineSearchAction="None"
         subcycling="1"
         nonlinearAccelerationType="Aitken"/>
-      <LinearSolverParameters
-        solverType="gmres"
-        preconditionerType="mgr"
-        logLevel="1"
-        krylovTol="1.0e-6"
-        krylovMaxIter="100"/>
     </SinglePhasePoromechanics>
     <!-- SPHINX_POROMECHANICSSOLVER_END -->
 
@@ -36,10 +30,8 @@
         newtonTol="1.0e-7"
         newtonMaxIter="40"/>
       <LinearSolverParameters
-        solverType="gmres"
-        preconditionerType="amg"
-        krylovTol="1.0e-6"
-        logLevel="1"/>
+        solverType="direct"
+        directParallel="0"/>
     </SolidMechanicsLagrangianSSLE>      
     <!-- SPHINX_MECHANICALSOLVER_END -->
 
@@ -54,10 +46,8 @@
         newtonTol="1.0e-7"
         newtonMaxIter="40"/>
       <LinearSolverParameters
-        solverType="gmres"
-        preconditionerType="amg"
-        krylovTol="1.0e-6"
-        logLevel="1"/>
+        solverType="direct"
+        directParallel="0"/>
     </SinglePhaseFVM>
     <!-- SPHINX_SINGLEPHASEFVM_END -->
 
@@ -89,15 +79,13 @@
       nx="{ 5, 11, 5 }"
       ny="{ 5, 11, 5 }"
       nz="{ 2, 5, 1, 1, 1, 1, 1 }"
-      cellBlockNames="{ b00,b01,b02,b03,b04,b05,b06,
-                        b07,b08,b09,b10,b11,b12,b13,
-                        b14,b15,b16,b17,b18,b19,b20, 
-                        b21,b22,b23,b24,b25,b26,b27,
-                        b28,b29,b30,b31,b32,b33,b34,
-                        b35,b36,b37,b38,b39,b40,b41,
-                        b42,b43,b44,b45,b46,b47,b48,
-                        b49,b50,b51,b52,b53,b54,b55,
-                        b56,b57,b58,b59,b60,b61,b62 }">
+      cellBlockNames="{ cb-0_0_0, cb-1_0_0, cb-2_0_0, cb-0_1_0, cb-1_1_0, cb-2_1_0, cb-0_2_0, cb-1_2_0, cb-2_2_0,
+                        cb-0_0_1, cb-1_0_1, cb-2_0_1, cb-0_1_1, cb-1_1_1, cb-2_1_1, cb-0_2_1, cb-1_2_1, cb-2_2_1,
+                        cb-0_0_2, cb-1_0_2, cb-2_0_2, cb-0_1_2, cb-1_1_2, cb-2_1_2, cb-0_2_2, cb-1_2_2, cb-2_2_2,
+                        cb-0_0_3, cb-1_0_3, cb-2_0_3, cb-0_1_3, cb-1_1_3, cb-2_1_3, cb-0_2_3, cb-1_2_3, cb-2_2_3,
+                        cb-0_0_4, cb-1_0_4, cb-2_0_4, cb-0_1_4, cb-1_1_4, cb-2_1_4, cb-0_2_4, cb-1_2_4, cb-2_2_4,
+                        cb-0_0_5, cb-1_0_5, cb-2_0_5, cb-0_1_5, cb-1_1_5, cb-2_1_5, cb-0_2_5, cb-1_2_5, cb-2_2_5,
+                        cb-0_0_6, cb-1_0_6, cb-2_0_6, cb-0_1_6, cb-1_1_6, cb-2_1_6, cb-0_2_6, cb-1_2_6, cb-2_2_6 }">
     </InternalMesh>
 
   </Mesh>
@@ -167,18 +155,16 @@
 
   <ElementRegions>
     <CellElementRegion name="extendedRegion"
-                  cellBlocks="{ b00,b01,b02,b03,b04,b05,b06,
-                                b07,b08,b09,b10,b11,b12,b13,
-                                b14,b15,b16,b17,b18,b19,b20, 
-                                b21,b22,b23,b24,b25,b26,b27,
-                                b28,    b30,b31,b32,b33,b34,
-                                b35,b36,b37,b38,b39,b40,b41,
-                                b42,b43,b44,b45,b46,b47,b48,
-                                b49,b50,b51,b52,b53,b54,b55,
-                                b56,b57,b58,b59,b60,b61,b62 }"
+                  cellBlocks="{ cb-0_0_0, cb-1_0_0, cb-2_0_0, cb-0_1_0, cb-1_1_0, cb-2_1_0, cb-0_2_0, cb-1_2_0, cb-2_2_0,
+                                cb-0_0_1, cb-1_0_1, cb-2_0_1, cb-0_1_1,           cb-2_1_1, cb-0_2_1, cb-1_2_1, cb-2_2_1,
+                                cb-0_0_2, cb-1_0_2, cb-2_0_2, cb-0_1_2, cb-1_1_2, cb-2_1_2, cb-0_2_2, cb-1_2_2, cb-2_2_2,
+                                cb-0_0_3, cb-1_0_3, cb-2_0_3, cb-0_1_3, cb-1_1_3, cb-2_1_3, cb-0_2_3, cb-1_2_3, cb-2_2_3,
+                                cb-0_0_4, cb-1_0_4, cb-2_0_4, cb-0_1_4, cb-1_1_4, cb-2_1_4, cb-0_2_4, cb-1_2_4, cb-2_2_4,
+                                cb-0_0_5, cb-1_0_5, cb-2_0_5, cb-0_1_5, cb-1_1_5, cb-2_1_5, cb-0_2_5, cb-1_2_5, cb-2_2_5,
+                                cb-0_0_6, cb-1_0_6, cb-2_0_6, cb-0_1_6, cb-1_1_6, cb-2_1_6, cb-0_2_6, cb-1_2_6, cb-2_2_6 }"
                   materialList="{fluid, porousRockExt}"/>
     <CellElementRegion name="reservoir"
-                  cellBlocks="{ b29 }"
+                  cellBlocks="{ cb-1_1_1 }"
                   materialList="{ fluid, porousRockRes }"/>
 
 
@@ -195,7 +181,7 @@
 
   <Events
       minTime="0"
-      maxTime="8640000">
+      maxTime="3456000">
    
     <PeriodicEvent
       name="outputs"
@@ -224,7 +210,7 @@
 
     <PeriodicEvent
       name="restarts"
-      timeFrequency="4320000"
+      timeFrequency="1728000"
       target="/Outputs/restartOutput"/>
 
   </Events>
@@ -391,7 +377,7 @@
       name="sigma_xx_Res"
       initialCondition="1"
       setNames="{ all }"
-      objectPath="ElementRegions/reservoir/b29"
+      objectPath="ElementRegions/reservoir/cb-1_1_1"
       fieldName="skeletonRes_stress"
       component="0"
       scale="0.0"/>
@@ -407,7 +393,7 @@
       name="sigma_yy_Res"
       initialCondition="1"
       setNames="{ all }"
-      objectPath="ElementRegions/reservoir/b29"
+      objectPath="ElementRegions/reservoir/cb-1_1_1"
       fieldName="skeletonRes_stress"
       component="1"
       scale="0.0"/>
@@ -423,7 +409,7 @@
       name="sigma_zz_Res"
       initialCondition="1"
       setNames="{ all }"
-      objectPath="ElementRegions/reservoir/b29"
+      objectPath="ElementRegions/reservoir/cb-1_1_1"
       fieldName="skeletonRes_stress"
       component="2"
       scale="0.0"/>
@@ -463,7 +449,7 @@
 
     <SourceFlux
       name="sourceTerm"
-      objectPath="ElementRegions/reservoir/b29"
+      objectPath="ElementRegions/reservoir/cb-1_1_1"
       scale="-1.84E+01"
       setNames="{ source }"/>
 
@@ -481,7 +467,7 @@
 
     <PackCollection
       name="pressureCollection"
-      objectPath="ElementRegions/reservoir/b29"
+      objectPath="ElementRegions/reservoir/cb-1_1_1"
       fieldName="pressure"/>
 
   </Tasks>
diff --git a/inputFiles/singlePhaseFlow/compressible_1d_2solids.xml b/inputFiles/singlePhaseFlow/compressible_1d_2solids.xml
index 1f28c8d3e13..b6c38999957 100644
--- a/inputFiles/singlePhaseFlow/compressible_1d_2solids.xml
+++ b/inputFiles/singlePhaseFlow/compressible_1d_2solids.xml
@@ -25,7 +25,7 @@
       nx="{ 5, 5 }"
       ny="{ 1 }"
       nz="{ 1 }"
-      cellBlockNames="{ block1, block2 }"/>
+      cellBlockNames="{ cb-0_0_0, cb-1_0_0 }"/>
   </Mesh>
 
   <Geometry>
@@ -69,12 +69,12 @@
   <ElementRegions>
     <CellElementRegion
       name="Region1"
-      cellBlocks="{ block1 }"
+      cellBlocks="{ cb-0_0_0 }"
       materialList="{ fluid, rock1 }"/>
 
     <CellElementRegion
       name="Region2"
-      cellBlocks="{ block2 }"
+      cellBlocks="{ cb-1_0_0 }"
       materialList="{ fluid, rock2 }"/>
   </ElementRegions>
 
diff --git a/inputFiles/singlePhaseFlow/compressible_2d_2fluids.xml b/inputFiles/singlePhaseFlow/compressible_2d_2fluids.xml
index 96110f04bbf..17b28f92439 100644
--- a/inputFiles/singlePhaseFlow/compressible_2d_2fluids.xml
+++ b/inputFiles/singlePhaseFlow/compressible_2d_2fluids.xml
@@ -25,7 +25,7 @@
       nx="{ 5, 5 }"
       ny="{ 3 }"
       nz="{ 1 }"
-      cellBlockNames="{ block1, block2 }"/>
+      cellBlockNames="{ cb-0_0_0, cb-1_0_0 }"/>
   </Mesh>
 
   <Geometry>
@@ -85,12 +85,12 @@
   <ElementRegions>
     <CellElementRegion
       name="Region1"
-      cellBlocks="{ block1 }"
+      cellBlocks="{ cb-0_0_0 }"
       materialList="{ fluid1, rock }"/>
 
     <CellElementRegion
       name="Region2"
-      cellBlocks="{ block2 }"
+      cellBlocks="{ cb-1_0_0 }"
       materialList="{ fluid2, rock }"/>
   </ElementRegions>
 
diff --git a/inputFiles/singlePhaseFlow/compressible_2d_2fluids_hybrid.xml b/inputFiles/singlePhaseFlow/compressible_2d_2fluids_hybrid.xml
index 2c934611c49..c7589636004 100644
--- a/inputFiles/singlePhaseFlow/compressible_2d_2fluids_hybrid.xml
+++ b/inputFiles/singlePhaseFlow/compressible_2d_2fluids_hybrid.xml
@@ -25,7 +25,7 @@
       nx="{ 5, 5 }"
       ny="{ 3 }"
       nz="{ 1 }"
-      cellBlockNames="{ block1, block2 }"/>
+      cellBlockNames="{ cb-0_0_0, cb-1_0_0 }"/>
   </Mesh>
 
   <Geometry>
@@ -85,12 +85,12 @@
   <ElementRegions>
     <CellElementRegion
       name="Region1"
-      cellBlocks="{ block1 }"
+      cellBlocks="{ cb-0_0_0 }"
       materialList="{ fluid1, rock }"/>
 
     <CellElementRegion
       name="Region2"
-      cellBlocks="{ block2 }"
+      cellBlocks="{ cb-1_0_0 }"
       materialList="{ fluid2, rock }"/>
   </ElementRegions>
 
@@ -137,7 +137,7 @@
       name="Porosity"
       initialCondition="1"
       setNames="{ all }"
-      objectPath="ElementRegions/Region1/block1"
+      objectPath="ElementRegions/Region1/cb-0_0_0"
       fieldName="rockPorosity_referencePorosity"
       scale="0.05"/>
 
diff --git a/inputFiles/singlePhaseFlow/staircase_3d.xml b/inputFiles/singlePhaseFlow/staircase_3d.xml
index 95628bc339d..199f1a726ea 100644
--- a/inputFiles/singlePhaseFlow/staircase_3d.xml
+++ b/inputFiles/singlePhaseFlow/staircase_3d.xml
@@ -25,7 +25,10 @@
       nx="{ 5, 5 }"
       ny="{ 5, 5 }"
       nz="{ 3, 3, 3, 3 }"
-      cellBlockNames="{ b00, b01, b02, b03, b04, b05, b06, b07, b08, b09, b10, b11, b12, b13, b14, b15 }"/>
+      cellBlockNames="{ cb-0_0_0, cb-1_0_0, cb-0_1_0, cb-1_1_0,
+                        cb-0_0_1, cb-1_0_1, cb-0_1_1, cb-1_1_1,
+                        cb-0_0_2, cb-1_0_2, cb-0_1_2, cb-1_1_2,
+                        cb-0_0_3, cb-1_0_3, cb-0_1_3, cb-1_1_3 }"/>
   </Mesh>
 
   <Geometry>
@@ -73,12 +76,12 @@
   <ElementRegions>
     <CellElementRegion
       name="Channel"
-      cellBlocks="{ b08, b00, b01, b05, b06, b14, b15, b11 }"
+      cellBlocks="{ cb-1_0_0, cb-0_0_0, cb-0_0_1, cb-0_1_1, cb-0_1_2, cb-1_1_2, cb-1_1_3, cb-1_0_3 }"
       materialList="{ water, rock }"/>
 
     <CellElementRegion
       name="Barrier"
-      cellBlocks="{ b04, b12, b13, b09, b10, b02, b03, b07 }"
+      cellBlocks="{ cb-0_1_0, cb-1_1_0, cb-1_1_1, cb-1_0_1, cb-1_0_2, cb-0_0_2, cb-0_0_3, cb-0_1_3 }"
       materialList="{ }"/>
   </ElementRegions>
 
diff --git a/inputFiles/singlePhaseWell/staircase_single_phase_wells_3d.xml b/inputFiles/singlePhaseWell/staircase_single_phase_wells_3d.xml
index 00d189ec214..6789ab90542 100644
--- a/inputFiles/singlePhaseWell/staircase_single_phase_wells_3d.xml
+++ b/inputFiles/singlePhaseWell/staircase_single_phase_wells_3d.xml
@@ -51,7 +51,10 @@
       nx="{ 5, 5 }"
       ny="{ 5, 5 }"
       nz="{ 3, 3, 3, 3 }"
-      cellBlockNames="{ b00, b01, b02, b03, b04, b05, b06, b07, b08, b09, b10, b11, b12, b13, b14, b15 }">
+      cellBlockNames="{ cb-0_0_0, cb-1_0_0, cb-0_1_0, cb-1_1_0,
+                        cb-0_0_1, cb-1_0_1, cb-0_1_1, cb-1_1_1,
+                        cb-0_0_2, cb-1_0_2, cb-0_1_2, cb-1_1_2,
+                        cb-0_0_3, cb-1_0_3, cb-0_1_3, cb-1_1_3 }">
 
       <InternalWell
         name="well_producer1"
@@ -105,12 +108,12 @@
   <ElementRegions>
     <CellElementRegion
       name="Channel"
-      cellBlocks="{ b08, b00, b01, b05, b06, b14, b15, b11 }"
+      cellBlocks="{ cb-1_0_0, cb-0_0_0, cb-0_0_1, cb-0_1_1, cb-0_1_2, cb-1_1_2, cb-1_1_3, cb-1_0_3 }"
       materialList="{ water, rock }"/>
 
     <CellElementRegion
       name="Barrier"
-      cellBlocks="{ b04, b12, b13, b09, b10, b02, b03, b07 }"
+      cellBlocks="{ cb-0_1_0, cb-1_1_0, cb-1_1_1, cb-1_0_1, cb-1_0_2, cb-0_0_2, cb-0_0_3, cb-0_1_3 }"
       materialList="{ }"/>
 
     <WellElementRegion
diff --git a/inputFiles/singlePhaseWell/staircase_single_phase_wells_hybrid_3d.xml b/inputFiles/singlePhaseWell/staircase_single_phase_wells_hybrid_3d.xml
index 9d2cb20066c..2298a32e483 100644
--- a/inputFiles/singlePhaseWell/staircase_single_phase_wells_hybrid_3d.xml
+++ b/inputFiles/singlePhaseWell/staircase_single_phase_wells_hybrid_3d.xml
@@ -54,7 +54,10 @@
       nx="{ 5, 5 }"
       ny="{ 5, 5 }"
       nz="{ 3, 3, 3, 3 }"
-      cellBlockNames="{ b00, b01, b02, b03, b04, b05, b06, b07, b08, b09, b10, b11, b12, b13, b14, b15 }">
+      cellBlockNames="{ cb-0_0_0, cb-1_0_0, cb-0_1_0, cb-1_1_0,
+                        cb-0_0_1, cb-1_0_1, cb-0_1_1, cb-1_1_1,
+                        cb-0_0_2, cb-1_0_2, cb-0_1_2, cb-1_1_2,
+                        cb-0_0_3, cb-1_0_3, cb-0_1_3, cb-1_1_3 }">
 
       <InternalWell
         name="well_producer1"
@@ -108,12 +111,12 @@
   <ElementRegions>
     <CellElementRegion
       name="Channel"
-      cellBlocks="{ b08, b00, b01, b05, b06, b14, b15, b11 }"
+      cellBlocks="{ cb-1_0_0, cb-0_0_0, cb-0_0_1, cb-0_1_1, cb-0_1_2, cb-1_1_2, cb-1_1_3, cb-1_0_3 }"
       materialList="{ water, rock }"/>
 
     <CellElementRegion
       name="Barrier"
-      cellBlocks="{ b04, b12, b13, b09, b10, b02, b03, b07 }"
+      cellBlocks="{ cb-0_1_0, cb-1_1_0, cb-1_1_1, cb-1_0_1, cb-1_0_2, cb-0_0_2, cb-0_0_3, cb-0_1_3 }"
       materialList="{ }"/>
 
     <WellElementRegion
diff --git a/inputFiles/solidMechanics/viscoExtendedDruckerPrager_relaxation_base.xml b/inputFiles/solidMechanics/viscoExtendedDruckerPrager_relaxation_base.xml
index 0afc57f9faa..a646a550529 100644
--- a/inputFiles/solidMechanics/viscoExtendedDruckerPrager_relaxation_base.xml
+++ b/inputFiles/solidMechanics/viscoExtendedDruckerPrager_relaxation_base.xml
@@ -38,7 +38,8 @@
   <ElementRegions>
     <CellElementRegion
       name="Domain"
-      cellBlocks="{ cb1, cb2, cb3, cb4, cb5, cb6, cb7, cb8 }"
+      cellBlocks="{ cb-0_0_0,  cb-1_0_0,  cb-0_1_0,  cb-1_1_0, 
+                    cb-0_0_1,  cb-1_0_1,  cb-0_1_1,  cb-1_1_1 }"
       materialList="{ rock }"/>
   </ElementRegions>
 <!-- SPHINX_ELEMENTREGIONS_END -->
@@ -155,7 +156,7 @@
   <Tasks>
     <PackCollection
       name="stressCollection"
-      objectPath="ElementRegions/Domain/cb8"
+      objectPath="ElementRegions/Domain/cb-1_1_1"
       fieldName="rock_stress"/> 
 
     <PackCollection
diff --git a/inputFiles/solidMechanics/viscoExtendedDruckerPrager_relaxation_benchmark.xml b/inputFiles/solidMechanics/viscoExtendedDruckerPrager_relaxation_benchmark.xml
index 475c0f4e668..605f41ca54c 100644
--- a/inputFiles/solidMechanics/viscoExtendedDruckerPrager_relaxation_benchmark.xml
+++ b/inputFiles/solidMechanics/viscoExtendedDruckerPrager_relaxation_benchmark.xml
@@ -16,7 +16,8 @@
       nx="{ 9, 1 }"
       ny="{ 9, 1 }"
       nz="{ 9, 1 }"
-      cellBlockNames="{ cb1, cb2, cb3, cb4, cb5, cb6, cb7, cb8 }"/>
+      cellBlockNames="{ cb-0_0_0,  cb-1_0_0,  cb-0_1_0,  cb-1_1_0, 
+                        cb-0_0_1,  cb-1_0_1,  cb-0_1_1,  cb-1_1_1 }"/>
   </Mesh>
 <!-- SPHINX_MESH_END -->
 
diff --git a/inputFiles/solidMechanics/viscoExtendedDruckerPrager_relaxation_smoke.xml b/inputFiles/solidMechanics/viscoExtendedDruckerPrager_relaxation_smoke.xml
index 0d50bd21c23..172adadc4f4 100644
--- a/inputFiles/solidMechanics/viscoExtendedDruckerPrager_relaxation_smoke.xml
+++ b/inputFiles/solidMechanics/viscoExtendedDruckerPrager_relaxation_smoke.xml
@@ -15,7 +15,8 @@
       nx="{ 1, 1 }"
       ny="{ 1, 1 }"
       nz="{ 1, 1 }"
-      cellBlockNames="{ cb1, cb2, cb3, cb4, cb5, cb6, cb7, cb8 }"/>
+      cellBlockNames="{ cb-0_0_0,  cb-1_0_0,  cb-0_1_0,  cb-1_1_0, 
+                        cb-0_0_1,  cb-1_0_1,  cb-0_1_1,  cb-1_1_1 }"/>
   </Mesh>
 
   <Events
diff --git a/inputFiles/thermoPoromechanics/ThermoPoroElastic_staircase_co2_smoke.xml b/inputFiles/thermoPoromechanics/ThermoPoroElastic_staircase_co2_smoke.xml
index 97101133740..19751f2670a 100644
--- a/inputFiles/thermoPoromechanics/ThermoPoroElastic_staircase_co2_smoke.xml
+++ b/inputFiles/thermoPoromechanics/ThermoPoroElastic_staircase_co2_smoke.xml
@@ -49,7 +49,10 @@
       nx="{ 3, 3 }"
       ny="{ 3, 3 }"
       nz="{ 2, 2, 2, 2 }"
-      cellBlockNames="{ b00, b01, b02, b03, b04, b05, b06, b07, b08, b09, b10, b11, b12, b13, b14, b15 }"/>
+      cellBlockNames="{ cb-0_0_0, cb-1_0_0, cb-0_1_0, cb-1_1_0,
+                        cb-0_0_1, cb-1_0_1, cb-0_1_1, cb-1_1_1,
+                        cb-0_0_2, cb-1_0_2, cb-0_1_2, cb-1_1_2,
+			cb-0_0_3, cb-1_0_3, cb-0_1_3, cb-1_1_3 }"/>
   </Mesh>
 
   <Geometry>
@@ -131,11 +134,11 @@
   <ElementRegions>
     <CellElementRegion
       name="channel"
-      cellBlocks="{ b08, b00, b01, b05, b06, b14, b15, b11 }"
+      cellBlocks="{ cb-1_0_0, cb-0_0_0, cb-0_0_1, cb-0_1_1, cb-0_1_2, cb-1_1_2, cb-1_1_3, cb-1_0_3 }"
       materialList="{ fluid, porousRockChannel, relperm, thermalCond }"/>
     <CellElementRegion
       name="barrier"
-      cellBlocks="{ b04, b12, b13, b09, b10, b02, b03, b07 }"
+      cellBlocks="{ cb-0_1_0, cb-1_1_0, cb-1_1_1, cb-1_0_1, cb-1_0_2, cb-0_0_2, cb-0_0_3, cb-0_1_3 }"
       materialList="{ fluid, porousRockBarrier, relperm, thermalCond }"/>
   </ElementRegions>
 
diff --git a/inputFiles/wavePropagation/acous3D_pml_smoke.xml b/inputFiles/wavePropagation/acous3D_pml_smoke.xml
index 7e2b978d31d..3a1e3db0f47 100644
--- a/inputFiles/wavePropagation/acous3D_pml_smoke.xml
+++ b/inputFiles/wavePropagation/acous3D_pml_smoke.xml
@@ -31,15 +31,15 @@
       nx="{ 1, 3, 1}"
       ny="{ 1, 3, 1}"
       nz="{ 1, 3, 1}"
-      cellBlockNames="{ pmlLeftFrontBottom, pmlLeftFrontMid, pmlLeftFrontTop,
-                        pmlLeftMidBottom, pmlLeftMidMid, pmlLeftMidTop,
-                        pmlLeftBackBottom, pmlLeftBackMid, pmlLeftBackTop,
-                        pmlMidFrontBottom, pmlMidFrontMid, pmlMidFrontTop,
-                        pmlMidMidBottom, interiorMidMidMid, pmlMidMidTop,
-                        pmlMidBackBottom, pmlMidBackMid, pmlMidBackTop,
-                        pmlRightFrontBottom, pmlRightFrontMid, pmlRightFrontTop,
-                        pmlRightMidBottom, pmlRightMidMid, pmlRightMidTop,
-                        pmlRightBackBottom, pmlRightBackMid, pmlRightBackTop }"/>
+      cellBlockNames="{ cb-0_0_0, cb-1_0_0, cb-2_0_0, 
+                        cb-0_1_0, cb-1_1_0, cb-2_1_0, 
+                        cb-0_2_0, cb-1_2_0, cb-2_2_0, 
+                        cb-0_0_1, cb-1_0_1, cb-2_0_1, 
+                        cb-0_1_1, cb-1_1_1, cb-2_1_1, 
+                        cb-0_2_1, cb-1_2_1, cb-2_2_1, 
+                        cb-0_0_2, cb-1_0_2, cb-2_0_2, 
+                        cb-0_1_2, cb-1_1_2, cb-2_1_2, 
+			cb-0_2_2, cb-1_2_2, cb-2_2_2 }"/>
   </Mesh>
 
   <Geometry>
@@ -115,20 +115,20 @@
     <!-- assign the interior and PML blocks to separate cell element regions -->
     <CellElementRegion
       name="interiorDomain"
-      cellBlocks="{ interiorMidMidMid }"
+      cellBlocks="{ cb-1_1_1 }"
       materialList="{ nullModel }"/>
 
     <CellElementRegion
       name="pmlDomain"
-      cellBlocks="{ pmlLeftFrontBottom, pmlLeftFrontMid, pmlLeftFrontTop,
-                        pmlLeftMidBottom, pmlLeftMidMid, pmlLeftMidTop,
-                        pmlLeftBackBottom, pmlLeftBackMid, pmlLeftBackTop,
-                        pmlMidFrontBottom, pmlMidFrontMid, pmlMidFrontTop,
-                        pmlMidMidBottom, pmlMidMidTop,
-                        pmlMidBackBottom, pmlMidBackMid, pmlMidBackTop,
-                        pmlRightFrontBottom, pmlRightFrontMid, pmlRightFrontTop,
-                        pmlRightMidBottom, pmlRightMidMid, pmlRightMidTop,
-                        pmlRightBackBottom, pmlRightBackMid, pmlRightBackTop }"
+      cellBlocks="{ cb-0_0_0, cb-1_0_0, cb-2_0_0, 
+                    cb-0_1_0, cb-1_1_0, cb-2_1_0, 
+                    cb-0_2_0, cb-1_2_0, cb-2_2_0, 
+                    cb-0_0_1, cb-1_0_1, cb-2_0_1, 
+                    cb-0_1_1,           cb-2_1_1, 
+                    cb-0_2_1, cb-1_2_1, cb-2_2_1, 
+                    cb-0_0_2, cb-1_0_2, cb-2_0_2, 
+                    cb-0_1_2, cb-1_1_2, cb-2_1_2, 
+                    cb-0_2_2, cb-1_2_2, cb-2_2_2 }"
       materialList="{ nullModel }"/>
   </ElementRegions>
 
diff --git a/integratedTests b/integratedTests
index abea2ddbfab..b50e624e7d9 160000
--- a/integratedTests
+++ b/integratedTests
@@ -1 +1 @@
-Subproject commit abea2ddbfab58ba445a9254d514dd5ac392a25ee
+Subproject commit b50e624e7d905faa2e4078e53162e159b75ebe6a
diff --git a/src/coreComponents/mesh/docs/Mesh.rst b/src/coreComponents/mesh/docs/Mesh.rst
index d4231f7ac20..c87441015b4 100644
--- a/src/coreComponents/mesh/docs/Mesh.rst
+++ b/src/coreComponents/mesh/docs/Mesh.rst
@@ -121,15 +121,18 @@ with the following code.
                   nx="{5, 5}"
                   ny="{5, 5}"
                   nz="{3, 3, 3, 3}"
-                  cellBlockNames="{b00,b01,b02,b03,b04,b05,b06,b07,b08,b09,b10,b11,b12,b13,b14,b15}"/>
+                  cellBlockNames="{cb-0_0_0, cb-1_0_0, cb-0_1_0, cb-1_1_0,
+                                   cb-0_0_1, cb-1_0_1, cb-0_1_1, cb-1_1_1,
+                                   cb-0_0_2, cb-1_0_2, cb-0_1_2, cb-1_1_2,
+                                   cb-0_0_3, cb-1_0_3, cb-0_1_3, cb-1_1_3}"/>
   </Mesh>
 
   <ElementRegions>
      <CellElementRegion name="Channel"
-                    cellBlocks="{b08,b00,b01,b05,b06,b14,b15,b11}"
+                    cellBlocks="{cb-1_0_0, cb-0_0_0, cb-0_0_1, cb-0_1_1, cb-0_1_2, cb-1_1_2, cb-1_1_3, cb-1_0_3}"
                     materialList="{fluid1, rock, relperm}"/>
      <CellElementRegion name="Barrier"
-                    cellBlocks="{b04,b12,b13,b09,b10,b02,b03,b07}"
+                    cellBlocks="{cb-0_1_0, cb-1_1_0, cb-1_1_1, cb-1_0_1, cb-1_0_2, cb-0_0_2, cb-0_0_3, cb-0_1_3}"
                     materialList="{}"/>
   </ElementRegions>
 
@@ -139,6 +142,7 @@ Thus, the generated mesh will be :
    :align: center
    :width: 500
 
+Note that ``CellBlocks`` are ordered following the natural IJK logic, with indices increasing first in I (x-direction), then in J (y-direction) and last in K (z-direction).
 
 .. _ExternalMeshUsage:
 
diff --git a/src/coreComponents/mesh/docs/staircase.svg b/src/coreComponents/mesh/docs/staircase.svg
index bda6f11f955..4a5dffd595d 100644
--- a/src/coreComponents/mesh/docs/staircase.svg
+++ b/src/coreComponents/mesh/docs/staircase.svg
@@ -2,24 +2,24 @@
 <!-- Created with Inkscape (http://www.inkscape.org/) -->
 
 <svg
-   xmlns:dc="http://purl.org/dc/elements/1.1/"
-   xmlns:cc="http://creativecommons.org/ns#"
-   xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
-   xmlns:svg="http://www.w3.org/2000/svg"
-   xmlns="http://www.w3.org/2000/svg"
-   xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
-   xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
    width="413.08026mm"
    height="362.52155mm"
    viewBox="0 0 413.08026 362.52156"
    version="1.1"
    id="svg8"
-   inkscape:version="0.92.4 5da689c313, 2019-01-14"
+   inkscape:version="1.3.2 (091e20e, 2023-11-25)"
    sodipodi:docname="staircase.svg"
    style="enable-background:new"
    inkscape:export-filename="/home/amazuyer/Pictures/staircase.png"
    inkscape:export-xdpi="96"
-   inkscape:export-ydpi="96">
+   inkscape:export-ydpi="96"
+   xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
+   xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
+   xmlns="http://www.w3.org/2000/svg"
+   xmlns:svg="http://www.w3.org/2000/svg"
+   xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
+   xmlns:cc="http://creativecommons.org/ns#"
+   xmlns:dc="http://purl.org/dc/elements/1.1/">
   <defs
      id="defs2" />
   <sodipodi:namedview
@@ -29,24 +29,27 @@
      borderopacity="1.0"
      inkscape:pageopacity="1"
      inkscape:pageshadow="2"
-     inkscape:zoom="0.401922"
-     inkscape:cx="903.8954"
-     inkscape:cy="632.38391"
+     inkscape:zoom="0.36802093"
+     inkscape:cx="748.59873"
+     inkscape:cy="528.50255"
      inkscape:document-units="mm"
-     inkscape:current-layer="layer4"
+     inkscape:current-layer="layer1"
      showgrid="false"
-     inkscape:window-width="1920"
-     inkscape:window-height="1007"
-     inkscape:window-x="0"
-     inkscape:window-y="0"
-     inkscape:window-maximized="1"
+     inkscape:window-width="1312"
+     inkscape:window-height="820"
+     inkscape:window-x="45"
+     inkscape:window-y="38"
+     inkscape:window-maximized="0"
      showguides="false"
      inkscape:snap-object-midpoints="true"
      fit-margin-top="0"
      fit-margin-left="0"
      fit-margin-right="0"
      fit-margin-bottom="0"
-     inkscape:object-paths="true" />
+     inkscape:object-paths="true"
+     inkscape:showpageshadow="2"
+     inkscape:pagecheckerboard="0"
+     inkscape:deskcolor="#d1d1d1" />
   <metadata
      id="metadata5">
     <rdf:RDF>
@@ -55,7 +58,7 @@
         <dc:format>image/svg+xml</dc:format>
         <dc:type
            rdf:resource="http://purl.org/dc/dcmitype/StillImage" />
-        <dc:title></dc:title>
+        <dc:title />
       </cc:Work>
     </rdf:RDF>
   </metadata>
@@ -1611,263 +1614,280 @@
      transform="translate(433.05483,92.624135)">
     <text
        id="text1281"
-       y="147.56969"
-       x="-312.34894"
-       style="font-style:normal;font-weight:normal;font-size:10.58333302px;line-height:1.25;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.26458332"
+       y="149.19183"
+       x="-325.92758"
+       style="font-style:normal;font-weight:normal;font-size:10.5833px;line-height:1.25;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
        xml:space="preserve"
        inkscape:export-xdpi="96"
        inkscape:export-ydpi="96"><tspan
-         style="stroke-width:0.26458332"
-         y="147.56969"
-         x="-312.34894"
+         style="stroke-width:0.264583"
+         y="149.19183"
+         x="-325.92758"
          id="tspan1279"
-         sodipodi:role="line">b00</tspan></text>
+         sodipodi:role="line">cb_0-0-0</tspan></text>
     <text
        id="text1285"
-       y="104.77562"
-       x="-311.46527"
-       style="font-style:normal;font-weight:normal;font-size:10.58333302px;line-height:1.25;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.26458332"
+       y="104.96862"
+       x="-325.92758"
+       style="font-style:normal;font-weight:normal;font-size:10.5833px;line-height:1.25;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
        xml:space="preserve"
        inkscape:export-xdpi="96"
        inkscape:export-ydpi="96"><tspan
-         style="stroke-width:0.26458332"
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diff --git a/src/coreComponents/mesh/generators/InternalMeshGenerator.cpp b/src/coreComponents/mesh/generators/InternalMeshGenerator.cpp
index 23845ab3b8f..71410f24651 100644
--- a/src/coreComponents/mesh/generators/InternalMeshGenerator.cpp
+++ b/src/coreComponents/mesh/generators/InternalMeshGenerator.cpp
@@ -585,54 +585,54 @@ void InternalMeshGenerator::fillCellBlockManager( CellBlockManager & cellBlockMa
 
   // Find elemCenters for even uniform element sizes
   array1d< array1d< real64 > > elemCenterCoords( 3 );
-  for( int i = 0; i < 3; ++i )
+  for( int dim = 0; dim < m_dim; ++dim )
   {
-    m_numElemsTotal[i] = 0;
-    for( int block = 0; block < m_nElems[i].size(); ++block )
+    m_numElemsTotal[dim] = 0;
+    for( int block = 0; block < m_nElems[dim].size(); ++block )
     {
-      m_numElemsTotal[i] += m_nElems[i][block];
+      m_numElemsTotal[dim] += m_nElems[dim][block];
     }
     array1d< int > const & parts = partition.getPartitions();
-    GEOS_ERROR_IF( parts[i] > m_numElemsTotal[i], "Number of partitions in a direction should not exceed the number of elements in that direction" );
+    GEOS_ERROR_IF( parts[dim] > m_numElemsTotal[dim], "Number of partitions in a direction should not exceed the number of elements in that direction" );
 
-    elemCenterCoords[i].resize( m_numElemsTotal[i] );
-    array1d< real64 > elemCenterCoordsLocal( m_numElemsTotal[i] );
-    for( int k = 0; k < m_numElemsTotal[i]; ++k )
+    elemCenterCoords[dim].resize( m_numElemsTotal[dim] );
+    array1d< real64 > elemCenterCoordsLocal( m_numElemsTotal[dim] );
+    for( integer k = 0; k < m_numElemsTotal[dim]; ++k )
     {
-      elemCenterCoordsLocal[k] = m_min[i] + ( m_max[i] - m_min[i] ) * ( k + 0.5 ) / m_numElemsTotal[i];
+      elemCenterCoordsLocal[k] = m_min[dim] + ( m_max[dim] - m_min[dim] ) * ( k + 0.5 ) / m_numElemsTotal[dim];
     }
     MpiWrapper::allReduce( elemCenterCoordsLocal.data(),
-                           elemCenterCoords[i].data(),
-                           m_numElemsTotal[i],
+                           elemCenterCoords[dim].data(),
+                           m_numElemsTotal[dim],
                            MPI_MAX,
                            MPI_COMM_GEOSX );
   }
 
   // Find starting/ending index
   // Get the first and last indices in this partition each direction
-  int firstElemIndexInPartition[3] = { -1, -1, -1 };
-  int lastElemIndexInPartition[3] = { -2, -2, -2 };
+  integer firstElemIndexInPartition[3] = { -1, -1, -1 };
+  integer lastElemIndexInPartition[3] = { -2, -2, -2 };
 
-  for( int i = 0; i < 3; ++i )
+  for( int dim = 0; dim < m_dim; ++dim )
   {
     //    firstElemIndexInPartition[i] = -1;
     //    lastElemIndexInPartition[i] = -2;
-    for( int k = 0; k < m_numElemsTotal[i]; ++k )
+    for( int k = 0; k < m_numElemsTotal[dim]; ++k )
     {
-      if( partition.isCoordInPartition( elemCenterCoords[i][k], i ) )
+      if( partition.isCoordInPartition( elemCenterCoords[dim][k], dim ) )
       {
-        firstElemIndexInPartition[i] = k;
+        firstElemIndexInPartition[dim] = k;
         break;
       }
     }
 
-    if( firstElemIndexInPartition[i] > -1 )
+    if( firstElemIndexInPartition[dim] > -1 )
     {
-      for( int k = firstElemIndexInPartition[i]; k < m_numElemsTotal[i]; ++k )
+      for( int k = firstElemIndexInPartition[dim]; k < m_numElemsTotal[dim]; ++k )
       {
-        if( partition.isCoordInPartition( elemCenterCoords[i][k], i ) )
+        if( partition.isCoordInPartition( elemCenterCoords[dim][k], dim ) )
         {
-          lastElemIndexInPartition[i] = k;
+          lastElemIndexInPartition[dim] = k;
         }
       }
     }
@@ -647,28 +647,28 @@ void InternalMeshGenerator::fillCellBlockManager( CellBlockManager & cellBlockMa
   array1d< integer > firstElemIndexForBlockInPartition[3];
   array1d< integer > lastElemIndexForBlockInPartition[3];
 
-  for( int dir = 0; dir < 3; ++dir )
+  for( int dim = 0; dim < 3; ++dim )
   {
-    firstElemIndexForBlockInPartition[dir] = m_firstElemIndexForBlock[dir];
-    lastElemIndexForBlockInPartition[dir] = m_lastElemIndexForBlock[dir];
+    firstElemIndexForBlockInPartition[dim] = m_firstElemIndexForBlock[dim];
+    lastElemIndexForBlockInPartition[dim] = m_lastElemIndexForBlock[dim];
 
-    for( int block = 0; block < m_nElems[dir].size(); ++block )
+    for( integer block = 0; block < m_nElems[dim].size(); ++block )
     {
-      if( firstElemIndexForBlockInPartition[dir][block] > lastElemIndexInPartition[dir] ||
-          lastElemIndexForBlockInPartition[dir][block] < firstElemIndexInPartition[dir] )
+      if( firstElemIndexForBlockInPartition[dim][block] > lastElemIndexInPartition[dim] ||
+          lastElemIndexForBlockInPartition[dim][block] < firstElemIndexInPartition[dim] )
       {
-        firstElemIndexForBlockInPartition[dir][block] = -1;
-        lastElemIndexForBlockInPartition[dir][block] = -2;
+        firstElemIndexForBlockInPartition[dim][block] = -1;
+        lastElemIndexForBlockInPartition[dim][block] = -2;
       }
       else
       {
-        if( firstElemIndexForBlockInPartition[dir][block] < firstElemIndexInPartition[dir] )
+        if( firstElemIndexForBlockInPartition[dim][block] < firstElemIndexInPartition[dim] )
         {
-          firstElemIndexForBlockInPartition[dir][block] = firstElemIndexInPartition[dir];
+          firstElemIndexForBlockInPartition[dim][block] = firstElemIndexInPartition[dim];
         }
-        if( lastElemIndexForBlockInPartition[dir][block] > lastElemIndexInPartition[dir] )
+        if( lastElemIndexForBlockInPartition[dim][block] > lastElemIndexInPartition[dim] )
         {
-          lastElemIndexForBlockInPartition[dir][block] = lastElemIndexInPartition[dir];
+          lastElemIndexForBlockInPartition[dim][block] = lastElemIndexInPartition[dim];
         }
       }
     }
@@ -676,11 +676,11 @@ void InternalMeshGenerator::fillCellBlockManager( CellBlockManager & cellBlockMa
 
   // TODO This needs to be rewritten for dimensions lower than 3.
   localIndex regionOffset = 0;
-  for( int iblock = 0; iblock < m_nElems[0].size(); ++iblock )
+  for( integer kblock = 0; kblock < m_nElems[2].size(); ++kblock )
   {
-    for( int jblock = 0; jblock < m_nElems[1].size(); ++jblock )
+    for( integer jblock = 0; jblock < m_nElems[1].size(); ++jblock )
     {
-      for( int kblock = 0; kblock < m_nElems[2].size(); ++kblock, ++regionOffset )
+      for( integer iblock = 0; iblock < m_nElems[0].size(); ++iblock, ++regionOffset )
       {
         numElemsInRegions[ m_regionNames[ regionOffset ] ] = 0;
         elemTypeInRegions[ m_regionNames[ regionOffset ] ] = ElementType::Quadrilateral;
@@ -691,13 +691,13 @@ void InternalMeshGenerator::fillCellBlockManager( CellBlockManager & cellBlockMa
   regionOffset = 0;
   {
     localIndex iR = 0;
-    for( int iblock = 0; iblock < m_nElems[0].size(); ++iblock )
+    for( integer kblock = 0; kblock < m_nElems[2].size(); ++kblock )
     {
-      for( int jblock = 0; jblock < m_nElems[1].size(); ++jblock )
+      for( integer jblock = 0; jblock < m_nElems[1].size(); ++jblock )
       {
-        for( int kblock = 0; kblock < m_nElems[2].size(); ++kblock, ++regionOffset, ++iR )
+        for( integer iblock = 0; iblock < m_nElems[0].size(); ++iblock, ++regionOffset, ++iR )
         {
-          int numElemsInRegion = 1;
+          integer numElemsInRegion = 1;
           numElemsInRegion *= lastElemIndexForBlockInPartition[0][iblock] - firstElemIndexForBlockInPartition[0][iblock] + 1;
 
           if( m_dim > 1 )
@@ -719,10 +719,9 @@ void InternalMeshGenerator::fillCellBlockManager( CellBlockManager & cellBlockMa
 
   localIndex numNodes = 1;
   integer numNodesInDir[3] = { 1, 1, 1 };
-
-  for( int i = 0; i < m_dim; ++i )
+  for( int dim = 0; dim < m_dim; ++dim )
   {
-    numNodesInDir[i] = lastElemIndexInPartition[i] - firstElemIndexInPartition[i] + 2;
+    numNodesInDir[dim] = lastElemIndexInPartition[dim] - firstElemIndexInPartition[dim] + 2;
   }
   reduceNumNodesForPeriodicBoundary( partition, numNodesInDir );
   numNodes = numNodesInDir[0] * numNodesInDir[1] * numNodesInDir[2];
@@ -735,17 +734,17 @@ void InternalMeshGenerator::fillCellBlockManager( CellBlockManager & cellBlockMa
 
   {
     localIndex localNodeIndex = 0;
-    for( int i = 0; i < numNodesInDir[0]; ++i )
+    for( integer k = 0; k < numNodesInDir[2]; ++k )
     {
-      for( int j = 0; j < numNodesInDir[1]; ++j )
+      for( integer j = 0; j < numNodesInDir[1]; ++j )
       {
-        for( int k = 0; k < numNodesInDir[2]; ++k )
+        for( integer i = 0; i < numNodesInDir[0]; ++i )
         {
-          int globalIJK[3] = { i, j, k };
+          integer globalIJK[3] = { i, j, k };
 
-          for( int a = 0; a < m_dim; ++a )
+          for( int dim = 0; dim < m_dim; ++dim )
           {
-            globalIJK[a] += firstElemIndexInPartition[a];
+            globalIJK[dim] += firstElemIndexInPartition[dim];
           }
 
           getNodePosition( globalIJK, m_trianglePattern, X[localNodeIndex] );
@@ -824,11 +823,11 @@ void InternalMeshGenerator::fillCellBlockManager( CellBlockManager & cellBlockMa
       numNodes = numNodesInDir[0] * numNodesInDir[1] * numNodesInDir[2];
     }
 
-    for( int iblock = 0; iblock < m_nElems[0].size(); ++iblock )
+    for( integer kblock = 0; kblock < m_nElems[2].size(); ++kblock )
     {
-      for( int jblock = 0; jblock < m_nElems[1].size(); ++jblock )
+      for( integer jblock = 0; jblock < m_nElems[1].size(); ++jblock )
       {
-        for( int kblock = 0; kblock < m_nElems[2].size(); ++kblock, ++regionOffset, ++iR )
+        for( integer iblock = 0; iblock < m_nElems[0].size(); ++iblock, ++regionOffset, ++iR )
         {
           ElementType const elementType = EnumStrings< ElementType >::fromString( m_elementType[iR] );
 
@@ -839,25 +838,25 @@ void InternalMeshGenerator::fillCellBlockManager( CellBlockManager & cellBlockMa
           arrayView2d< localIndex, cells::NODE_MAP_USD > elemsToNodes = cellBlock.getElemToNode();
           arrayView1d< globalIndex > const & elemLocalToGlobal = cellBlock.localToGlobalMap();
 
-          int numElemsInDirForBlock[3] =
+          integer numElemsInDirForBlock[3] =
           { lastElemIndexForBlockInPartition[0][iblock] - firstElemIndexForBlockInPartition[0][iblock] + 1,
             lastElemIndexForBlockInPartition[1][jblock] - firstElemIndexForBlockInPartition[1][jblock] + 1,
             lastElemIndexForBlockInPartition[2][kblock] - firstElemIndexForBlockInPartition[2][kblock] + 1 };
 
-          for( int i = 0; i < numElemsInDirForBlock[0]; ++i )
+          for( integer k = 0; k < numElemsInDirForBlock[2]; ++k )
           {
-            for( int j = 0; j < numElemsInDirForBlock[1]; ++j )
+            for( integer j = 0; j < numElemsInDirForBlock[1]; ++j )
             {
-              for( int k = 0; k < numElemsInDirForBlock[2]; ++k )
+              for( integer i = 0; i < numElemsInDirForBlock[0]; ++i )
               {
-                int globalIJK[3] =
+                integer globalIJK[3] =
                 { i + firstElemIndexForBlockInPartition[0][iblock],
                   j + firstElemIndexForBlockInPartition[1][jblock],
                   k + firstElemIndexForBlockInPartition[2][kblock] };
 
-                const localIndex firstNodeIndex = numNodesInDir[1] * numNodesInDir[2] * ( globalIJK[0] - firstElemIndexInPartition[0] )
-                                                  + numNodesInDir[2] * ( globalIJK[1] - firstElemIndexInPartition[1] )
-                                                  + ( globalIJK[2] - firstElemIndexInPartition[2] );
+                localIndex const firstNodeIndex = ( globalIJK[0] - firstElemIndexInPartition[0] )
+                                                  + numNodesInDir[0] * ( globalIJK[1] - firstElemIndexInPartition[1] )
+                                                  + numNodesInDir[0] * numNodesInDir[1] * ( globalIJK[2] - firstElemIndexInPartition[2] );
                 localIndex nodeOfBox[8];
 
                 if( elementType == ElementType::Quadrilateral || elementType == ElementType::Triangle )
@@ -869,15 +868,17 @@ void InternalMeshGenerator::fillCellBlockManager( CellBlockManager & cellBlockMa
                 }
                 else
                 {
+                  localIndex const stride[3] = { 1, numNodesInDir[0], numNodesInDir[0] * numNodesInDir[1] };
+
                   nodeOfBox[0] = firstNodeIndex;
-                  nodeOfBox[1] = numNodesInDir[1] * numNodesInDir[2] + firstNodeIndex;
-                  nodeOfBox[2] = numNodesInDir[1] * numNodesInDir[2] + numNodesInDir[2] + firstNodeIndex;
-                  nodeOfBox[3] = numNodesInDir[2] + firstNodeIndex;
+                  nodeOfBox[1] = nodeOfBox[0] + stride[0];
+                  nodeOfBox[2] = nodeOfBox[1] + stride[1];
+                  nodeOfBox[3] = nodeOfBox[0] + stride[1];
 
-                  nodeOfBox[4] = firstNodeIndex + 1;
-                  nodeOfBox[5] = numNodesInDir[1] * numNodesInDir[2] + firstNodeIndex + 1;
-                  nodeOfBox[6] = numNodesInDir[1] * numNodesInDir[2] + numNodesInDir[2] + firstNodeIndex + 1;
-                  nodeOfBox[7] = numNodesInDir[2] + firstNodeIndex + 1;
+                  nodeOfBox[4] = nodeOfBox[0] + stride[2];
+                  nodeOfBox[5] = nodeOfBox[1] + stride[2];
+                  nodeOfBox[6] = nodeOfBox[2] + stride[2];
+                  nodeOfBox[7] = nodeOfBox[3] + stride[2];
 
                   //               7___________________ 6
                   //               /                   /|
@@ -977,6 +978,8 @@ InternalMeshGenerator::
                                       int const (&firstElemIndexInPartition)[3],
                                       localIndex (& nodeOfBox)[8] )
 {
+  GEOS_ERROR_IF( component != 1, "Connectivity for periodic boundary implemented for the 1-component only" );
+
   // Condition is:
   // 1) element is last index in component direction
   // 2) first local element in component partition is zero
@@ -986,14 +989,14 @@ InternalMeshGenerator::
     // Last set of nodes
     int modGlobalIJK[3] = { globalIJK[0], globalIJK[1], globalIJK[2] };
     modGlobalIJK[component] = 0;
-    const localIndex firstNodeIndex = numNodesInDir[1] * numNodesInDir[2] * ( modGlobalIJK[0] - firstElemIndexInPartition[0] )
-                                      + numNodesInDir[2] * ( modGlobalIJK[1] - 0 )
-                                      + ( modGlobalIJK[2] - firstElemIndexInPartition[2] );
+    localIndex const firstNodeIndex = ( modGlobalIJK[0] - firstElemIndexInPartition[0] )
+                                      + numNodesInDir[0] * ( modGlobalIJK[1] - firstElemIndexInPartition[1] )
+                                      + numNodesInDir[0] * numNodesInDir[1] * ( modGlobalIJK[2] - firstElemIndexInPartition[2] );
 
     nodeOfBox[3] = firstNodeIndex;
-    nodeOfBox[2] = numNodesInDir[1] * numNodesInDir[2] + firstNodeIndex;
-    nodeOfBox[7] = firstNodeIndex + 1;
-    nodeOfBox[6] = numNodesInDir[1] * numNodesInDir[2] + firstNodeIndex + 1;
+    nodeOfBox[2] = nodeOfBox[3] + 1;
+    nodeOfBox[7] = nodeOfBox[3] + numNodesInDir[0] * numNodesInDir[1];
+    nodeOfBox[6] = nodeOfBox[7] + 1;
   }
 }
 
diff --git a/src/coreComponents/mesh/generators/InternalMeshGenerator.hpp b/src/coreComponents/mesh/generators/InternalMeshGenerator.hpp
index 9b95d975df9..bcb16630c92 100644
--- a/src/coreComponents/mesh/generators/InternalMeshGenerator.hpp
+++ b/src/coreComponents/mesh/generators/InternalMeshGenerator.hpp
@@ -271,7 +271,7 @@ class InternalMeshGenerator : public MeshGeneratorBase
    */
   inline globalIndex nodeGlobalIndex( int const index[3] )
   {
-    return index[0]*(m_numElemsTotal[1]+1)*(m_numElemsTotal[2]+1) + index[1]*(m_numElemsTotal[2]+1) + index[2];
+    return index[0] + index[1]*(m_numElemsTotal[0]+1) + index[2]*(m_numElemsTotal[0]+1)*(m_numElemsTotal[1]+1);
   }
 
   /**
@@ -280,7 +280,7 @@ class InternalMeshGenerator : public MeshGeneratorBase
    */
   inline globalIndex elemGlobalIndex( int const index[3] )
   {
-    return index[0]*m_numElemsTotal[1]*m_numElemsTotal[2] + index[1]*m_numElemsTotal[2] + index[2];
+    return index[0] + index[1]*m_numElemsTotal[0] + index[2]*m_numElemsTotal[0]*m_numElemsTotal[1];
   }
 
   /**
diff --git a/src/coreComponents/unitTests/meshTests/testMeshGeneration.cpp b/src/coreComponents/unitTests/meshTests/testMeshGeneration.cpp
index a2529c16406..e2891e9eb96 100644
--- a/src/coreComponents/unitTests/meshTests/testMeshGeneration.cpp
+++ b/src/coreComponents/unitTests/meshTests/testMeshGeneration.cpp
@@ -43,11 +43,11 @@ constexpr double dx = maxCoordInX / numElemsInX;
 constexpr double dy = maxCoordInY / numElemsInY;
 constexpr double dz = maxCoordInZ / numElemsInZ;
 
-constexpr localIndex node_dI = numNodesInY * numNodesInZ;
-constexpr localIndex node_dJ = numNodesInZ;
+constexpr localIndex node_dJ = numNodesInX;
+constexpr localIndex node_dK = numNodesInX * numNodesInY;
 
-constexpr localIndex elem_dI = numElemsInY * numElemsInZ;
-constexpr localIndex elem_dJ = numElemsInZ;
+constexpr localIndex elem_dJ = numElemsInX;
+constexpr localIndex elem_dK = numElemsInX * numElemsInY;
 
 constexpr localIndex minOrder = 1;
 constexpr localIndex maxOrder = 5;
@@ -151,11 +151,11 @@ TEST_F( MeshGenerationTest, nodePositions )
   arrayView2d< real64 const, nodes::REFERENCE_POSITION_USD > const & X = m_nodeManager->referencePosition();
 
   localIndex nodeIndex = 0;
-  for( localIndex i = 0; i < numNodesInX; ++i )
+  for( localIndex k = 0; k < numNodesInZ; ++k )
   {
     for( localIndex j = 0; j < numNodesInY; ++j )
     {
-      for( localIndex k = 0; k < numNodesInZ; ++k )
+      for( localIndex i = 0; i < numNodesInX; ++i )
       {
         EXPECT_DOUBLE_EQ( X( nodeIndex, 0 ), i * dx );
         EXPECT_DOUBLE_EQ( X( nodeIndex, 1 ), j * dy );
@@ -174,11 +174,11 @@ TEST_F( MeshGenerationTest, elementCentersAndVolumes )
   constexpr double VOLUME = dx * dy * dz;
 
   localIndex elemID = 0;
-  for( localIndex i = 0; i < numElemsInX; ++i )
+  for( localIndex k = 0; k < numElemsInZ; ++k )
   {
     for( localIndex j = 0; j < numElemsInY; ++j )
     {
-      for( localIndex k = 0; k < numElemsInZ; ++k )
+      for( localIndex i = 0; i < numElemsInX; ++i )
       {
         EXPECT_DOUBLE_EQ( centers[ elemID ][ 0 ], i * dx + dx / 2.0 );
         EXPECT_DOUBLE_EQ( centers[ elemID ][ 1 ], j * dy + dy / 2.0 );
@@ -196,23 +196,23 @@ TEST_F( MeshGenerationTest, elemToNodeMap )
   GEOS_ERROR_IF_NE( nodeMap.size( 1 ), 8 );
 
   localIndex elemID = 0;
-  for( localIndex i = 0; i < numElemsInX; ++i )
+  for( localIndex k = 0; k < numElemsInZ; ++k )
   {
     for( localIndex j = 0; j < numElemsInY; ++j )
     {
-      for( localIndex k = 0; k < numElemsInZ; ++k )
+      for( localIndex i = 0; i < numElemsInX; ++i )
       {
-        localIndex const firstNodeID = i * node_dI + j * node_dJ + k;
+        localIndex const firstNodeID = i + j * node_dJ + k * node_dK;
 
         EXPECT_EQ( firstNodeID, nodeMap( elemID, 0 ) );
-        EXPECT_EQ( firstNodeID + node_dI, nodeMap( elemID, 1 ) );
-        EXPECT_EQ( firstNodeID + node_dI + node_dJ, nodeMap( elemID, 3 ) );
+        EXPECT_EQ( firstNodeID + 1, nodeMap( elemID, 1 ) );
+        EXPECT_EQ( firstNodeID + 1 + node_dJ, nodeMap( elemID, 3 ) );
         EXPECT_EQ( firstNodeID + node_dJ, nodeMap( elemID, 2 ) );
 
-        EXPECT_EQ( firstNodeID + 1, nodeMap( elemID, 4 ) );
-        EXPECT_EQ( firstNodeID + 1 + node_dI, nodeMap( elemID, 5 ) );
-        EXPECT_EQ( firstNodeID + 1 + node_dI + node_dJ, nodeMap( elemID, 7 ) );
-        EXPECT_EQ( firstNodeID + 1 + node_dJ, nodeMap( elemID, 6 ) );
+        EXPECT_EQ( firstNodeID + node_dK, nodeMap( elemID, 4 ) );
+        EXPECT_EQ( firstNodeID + node_dK + 1, nodeMap( elemID, 5 ) );
+        EXPECT_EQ( firstNodeID + node_dK + 1 + node_dJ, nodeMap( elemID, 7 ) );
+        EXPECT_EQ( firstNodeID + node_dK + node_dJ, nodeMap( elemID, 6 ) );
         ++elemID;
       }
     }
@@ -224,13 +224,13 @@ TEST_F( MeshGenerationTest, nodeToElemMap )
   ArrayOfArraysView< localIndex const > const & nodeToElemMap = m_nodeManager->elementList().toViewConst();
 
   localIndex nodeIndex = 0;
-  for( localIndex i = 0; i < numNodesInX; ++i )
+  for( localIndex k = 0; k < numNodesInZ; ++k )
   {
     for( localIndex j = 0; j < numNodesInY; ++j )
     {
-      for( localIndex k = 0; k < numNodesInZ; ++k )
+      for( localIndex i = 0; i < numNodesInX; ++i )
       {
-        localIndex const elemID = i * elem_dI + j * elem_dJ + k;
+        localIndex const elemID = i + j * elem_dJ + k * elem_dK;
 
         std::vector< localIndex > expectedElems;
         if( k < numElemsInZ )
@@ -238,9 +238,9 @@ TEST_F( MeshGenerationTest, nodeToElemMap )
           if( i < numElemsInX && j < numElemsInY )
             expectedElems.push_back( elemID );
           if( i > 0 && j < numElemsInY )
-            expectedElems.push_back( elemID - elem_dI );
+            expectedElems.push_back( elemID - 1 );
           if( i > 0 && j > 0 )
-            expectedElems.push_back( elemID - elem_dI - elem_dJ );
+            expectedElems.push_back( elemID - 1 - elem_dJ );
           if( i < numElemsInX && j > 0 )
             expectedElems.push_back( elemID - elem_dJ );
         }
@@ -248,13 +248,13 @@ TEST_F( MeshGenerationTest, nodeToElemMap )
         if( k > 0 )
         {
           if( i < numElemsInX && j < numElemsInY )
-            expectedElems.push_back( elemID - 1 );
+            expectedElems.push_back( elemID - elem_dK );
           if( i > 0 && j < numElemsInY )
-            expectedElems.push_back( elemID - elem_dI - 1 );
+            expectedElems.push_back( elemID - elem_dK - 1 );
           if( i > 0 && j > 0 )
-            expectedElems.push_back( elemID - elem_dI - elem_dJ - 1 );
+            expectedElems.push_back( elemID - 1 - elem_dJ - elem_dK );
           if( i < numElemsInX && j > 0 )
-            expectedElems.push_back( elemID - elem_dJ - 1 );
+            expectedElems.push_back( elemID - elem_dJ - elem_dK );
         }
 
         localIndex const numElems = expectedElems.size();
@@ -290,11 +290,11 @@ TEST_F( MeshGenerationTest, faceNodeMaps )
   array1d< localIndex > faceNodesFromFace( 4 );
 
   localIndex elemID = 0;
-  for( localIndex i = 0; i < numElemsInX; ++i )
+  for( localIndex k = 0; k < numElemsInZ; ++k )
   {
     for( localIndex j = 0; j < numElemsInY; ++j )
     {
-      for( localIndex k = 0; k < numElemsInZ; ++k )
+      for( localIndex i = 0; i < numElemsInX; ++i )
       {
         for( localIndex f = 0; f < 6; ++f )
         {
@@ -340,14 +340,14 @@ TEST_F( MeshGenerationTest, faceElementMaps )
 
   GEOS_ERROR_IF_NE( elementToFaceMap.size( 1 ), 6 );
 
-  localIndex const elemIDOffset[6] = { -elem_dJ, -1, -elem_dI, elem_dI, elem_dJ, 1 };
+  localIndex const elemIDOffset[6] = { -elem_dJ, -elem_dK, -1, 1, elem_dJ, elem_dK };
 
   localIndex elemID = 0;
-  for( localIndex i = 0; i < numElemsInX; ++i )
+  for( localIndex k = 0; k < numElemsInZ; ++k )
   {
     for( localIndex j = 0; j < numElemsInY; ++j )
     {
-      for( localIndex k = 0; k < numElemsInZ; ++k )
+      for( localIndex i = 0; i < numElemsInX; ++i )
       {
         for( localIndex f = 0; f < 6; ++f )
         {
@@ -421,21 +421,21 @@ TEST_F( MeshGenerationTest, edgeNodeMaps )
   GEOS_ERROR_IF_NE( edgeToNodeMap.size( 1 ), 2 );
 
   localIndex nodeIndex = 0;
-  for( localIndex i = 0; i < numNodesInX; ++i )
+  for( localIndex k = 0; k < numNodesInZ; ++k )
   {
     for( localIndex j = 0; j < numNodesInY; ++j )
     {
-      for( localIndex k = 0; k < numNodesInZ; ++k )
+      for( localIndex i = 0; i < numNodesInX; ++i )
       {
         localIndex numEdges = 0;
         if( i != 0 )
         {
-          EXPECT_TRUE( walkEdgesToFindNeighbor( nodeIndex, nodeIndex - node_dI, nodeToEdgeMap[ nodeIndex ], edgeToNodeMap ) );
+          EXPECT_TRUE( walkEdgesToFindNeighbor( nodeIndex, nodeIndex - 1, nodeToEdgeMap[ nodeIndex ], edgeToNodeMap ) );
           ++numEdges;
         }
         if( i != numNodesInX - 1 )
         {
-          EXPECT_TRUE( walkEdgesToFindNeighbor( nodeIndex, nodeIndex + node_dI, nodeToEdgeMap[ nodeIndex ], edgeToNodeMap ) );
+          EXPECT_TRUE( walkEdgesToFindNeighbor( nodeIndex, nodeIndex + 1, nodeToEdgeMap[ nodeIndex ], edgeToNodeMap ) );
           ++numEdges;
         }
         if( j != 0 )
@@ -450,12 +450,12 @@ TEST_F( MeshGenerationTest, edgeNodeMaps )
         }
         if( k != 0 )
         {
-          EXPECT_TRUE( walkEdgesToFindNeighbor( nodeIndex, nodeIndex - 1, nodeToEdgeMap[ nodeIndex ], edgeToNodeMap ) );
+          EXPECT_TRUE( walkEdgesToFindNeighbor( nodeIndex, nodeIndex - node_dK, nodeToEdgeMap[ nodeIndex ], edgeToNodeMap ) );
           ++numEdges;
         }
         if( k != numNodesInZ - 1 )
         {
-          EXPECT_TRUE( walkEdgesToFindNeighbor( nodeIndex, nodeIndex + 1, nodeToEdgeMap[ nodeIndex ], edgeToNodeMap ) );
+          EXPECT_TRUE( walkEdgesToFindNeighbor( nodeIndex, nodeIndex + node_dK, nodeToEdgeMap[ nodeIndex ], edgeToNodeMap ) );
           ++numEdges;
         }
 
@@ -477,11 +477,11 @@ TEST_F( MeshGenerationTest, edgeFaceMaps )
   GEOS_ERROR_IF_NE( elementToFaceMap.size( 1 ), 6 );
 
   localIndex elemID = 0;
-  for( localIndex i = 0; i < numElemsInX; ++i )
+  for( localIndex k = 0; k < numElemsInZ; ++k )
   {
     for( localIndex j = 0; j < numElemsInY; ++j )
     {
-      for( localIndex k = 0; k < numElemsInZ; ++k )
+      for( localIndex i = 0; i < numElemsInX; ++i )
       {
         for( localIndex f = 0; f < 6; ++f )
         {
diff --git a/src/docs/sphinx/developerGuide/Contributing/IntegratedTests.rst b/src/docs/sphinx/developerGuide/Contributing/IntegratedTests.rst
index f2e355372c2..e8a97841ac2 100644
--- a/src/docs/sphinx/developerGuide/Contributing/IntegratedTests.rst
+++ b/src/docs/sphinx/developerGuide/Contributing/IntegratedTests.rst
@@ -542,11 +542,11 @@ To do this you can run this command in the build directory:
   make ats_rebaseline_failed
 
 
-Otherwise, you can run the following command, and select whether tests should be rebaselined one at a time via a ``[y/n]`` prompt.
+Otherwise, you can run the following command, and select whether tests should be rebaselined one at a time via a ``[y/n]`` prompt:
 
 .. code-block:: sh
 
-  make ats_rebaseline_failed
+  make ats_rebaseline
 
 
 Make sure to only answer ``y`` to the tests that you actually want to rebaseline, otherwise correct baselines for already passing tests will still be updated and bloat your pull request and repository size.