Node-level visualization support for coefficients of Subcell limiting

src/solvers/dg.jl

@@ -221,6 +221,12 @@ end
 
 function get_node_variables!(node_variables, mesh, equations,
                              volume_integral::VolumeIntegralSubcellLimiting, dg, cache)
+    # While for the element-wise limiting with `VolumeIntegralShockCapturingHG` the indicator is
+    # called here to get up-to-date values for IO, this is not easily possible in this case
+    # because the calculation is very integrated into the method.
+    # See also https://github.com/trixi-framework/Trixi.jl/pull/1611#discussion_r1334553206.
+    # Therefore, the coefficients at `t=t^{n-1}` are saved. Thus, the coefficients of the first
+    # stored solution (initial condition) are not yet defined and were manually set to `-1`.
     get_node_variables!(node_variables, volume_integral.limiter, volume_integral,
                         equations)
 end

src/solvers/dgsem_tree/containers_2d.jl

@@ -1372,7 +1372,7 @@ function Base.resize!(container::ContainerSubcellLimiterIDP2D, capacity)
     @unpack _alpha, _alpha1, _alpha2 = container
     resize!(_alpha, n_nodes * n_nodes * capacity)
     container.alpha = unsafe_wrap(Array, pointer(_alpha), (n_nodes, n_nodes, capacity))
-    container.alpha .= zero(eltype(container.alpha))
+    container.alpha .= -1 * one(eltype(container.alpha))
     resize!(_alpha1, (n_nodes + 1) * n_nodes * capacity)
     container.alpha1 = unsafe_wrap(Array, pointer(_alpha1),
                                    (n_nodes + 1, n_nodes, capacity))

src/solvers/dgsem_tree/subcell_limiters.jl

@@ -103,7 +103,7 @@ end
 
 function get_node_variables!(node_variables, limiter::SubcellLimiterIDP,
                              ::VolumeIntegralSubcellLimiting, equations)
-    node_variables[:alpha_limiter] = limiter.cache.subcell_limiter_coefficients.alpha
+    node_variables[:limiting_coefficient] = limiter.cache.subcell_limiter_coefficients.alpha
 
     return nothing
 end

src/time_integration/methods_SSP.jl

@@ -31,6 +31,11 @@ struct SimpleSSPRK33{StageCallbacks} <: SimpleAlgorithmSSP
     stage_callbacks::StageCallbacks
 
     function SimpleSSPRK33(; stage_callbacks = ())
+        # Mathematically speaking, it is not necessary for the algorithm to split the factors
+        # into numerator and denominator. Otherwise, however, rounding errors of the order of
+        # the machine accuracy will occur, which will add up over time and thus endanger the
+        # conservation of the simulation.
+        # See also https://github.com/trixi-framework/Trixi.jl/pull/1640.
         numerator_a = SVector(0.0, 3.0, 1.0) # a = numerator_a / denominator
         numerator_b = SVector(1.0, 1.0, 2.0) # b = numerator_b / denominator
         denominator = SVector(1.0, 4.0, 3.0)