Format & Comment custom integrators (trixi-framework#2218)

* Format & Comment custom integrators

* Update src/time_integration/methods_2N.jl

Co-authored-by: Joshua Lampert <[email protected]>

---------

Co-authored-by: Joshua Lampert <[email protected]>

Author: DanielDoehring

src/semidiscretization/semidiscretization_euler_gravity.jl

@@ -360,15 +360,21 @@ end
 function timestep_gravity_carpenter_kennedy_erk54_2N!(cache, u_euler, tau, dtau,
                                                       gravity_parameters, semi_gravity)
     # Coefficients for Carpenter's 5-stage 4th-order low-storage Runge-Kutta method
-    a = SVector(0.0, 567301805773.0 / 1357537059087.0,
+    a = SVector(0.0,
+                567301805773.0 / 1357537059087.0,
                 2404267990393.0 / 2016746695238.0,
-                3550918686646.0 / 2091501179385.0, 1275806237668.0 / 842570457699.0)
-    b = SVector(1432997174477.0 / 9575080441755.0, 5161836677717.0 / 13612068292357.0,
-                1720146321549.0 / 2090206949498.0, 3134564353537.0 / 4481467310338.0,
+                3550918686646.0 / 2091501179385.0,
+                1275806237668.0 / 842570457699.0)
+    b = SVector(1432997174477.0 / 9575080441755.0,
+                5161836677717.0 / 13612068292357.0,
+                1720146321549.0 / 2090206949498.0,
+                3134564353537.0 / 4481467310338.0,
                 2277821191437.0 / 14882151754819.0)
-    c = SVector(0.0, 1432997174477.0 / 9575080441755.0,
+    c = SVector(0.0,
+                1432997174477.0 / 9575080441755.0,
                 2526269341429.0 / 6820363962896.0,
-                2006345519317.0 / 3224310063776.0, 2802321613138.0 / 2924317926251.0)
+                2006345519317.0 / 3224310063776.0,
+                2802321613138.0 / 2924317926251.0)
 
     timestep_gravity_2N!(cache, u_euler, tau, dtau, gravity_parameters, semi_gravity,
                          a, b, c)

src/time_integration/methods_2N.jl

@@ -14,7 +14,10 @@ abstract type SimpleAlgorithm2N end
 The following structures and methods provide a minimal implementation of
 the low-storage explicit Runge-Kutta method of
 
-    Carpenter, Kennedy (1994) Fourth order 2N storage RK schemes, Solution 3
+- Carpenter, Kennedy (1994) 
+  Fourth-order 2N-storage Runge-Kutta schemes (Solution 3)
+  URL: https://ntrs.nasa.gov/citations/19940028444
+  File: https://ntrs.nasa.gov/api/citations/19940028444/downloads/19940028444.pdf
 
 using the same interface as OrdinaryDiffEq.jl.
 """
@@ -24,15 +27,18 @@ struct CarpenterKennedy2N54 <: SimpleAlgorithm2N
     c::SVector{5, Float64}
 
     function CarpenterKennedy2N54()
-        a = SVector(0.0, 567301805773.0 / 1357537059087.0,
+        a = SVector(0.0,
+                    567301805773.0 / 1357537059087.0,
                     2404267990393.0 / 2016746695238.0,
-                    3550918686646.0 / 2091501179385.0, 1275806237668.0 / 842570457699.0)
+                    3550918686646.0 / 2091501179385.0,
+                    1275806237668.0 / 842570457699.0)
         b = SVector(1432997174477.0 / 9575080441755.0,
                     5161836677717.0 / 13612068292357.0,
                     1720146321549.0 / 2090206949498.0,
                     3134564353537.0 / 4481467310338.0,
                     2277821191437.0 / 14882151754819.0)
-        c = SVector(0.0, 1432997174477.0 / 9575080441755.0,
+        c = SVector(0.0,
+                    1432997174477.0 / 9575080441755.0,
                     2526269341429.0 / 6820363962896.0,
                     2006345519317.0 / 3224310063776.0,
                     2802321613138.0 / 2924317926251.0)
@@ -42,9 +48,15 @@ struct CarpenterKennedy2N54 <: SimpleAlgorithm2N
 end
 
 """
-      CarpenterKennedy2N43()
+    CarpenterKennedy2N43()
 
-Carpenter, Kennedy (1994) Third order 2N storage RK schemes with error control
+The following structures and methods provide a minimal implementation of
+the low-storage explicit Runge-Kutta method of
+
+- Carpenter, Kennedy (1994) 
+  Third-order 2N-storage Runge-Kutta schemes with error control
+  URL: https://ntrs.nasa.gov/citations/19940028444
+  File: https://ntrs.nasa.gov/api/citations/19940028444/downloads/19940028444.pdf
 """
 struct CarpenterKennedy2N43 <: SimpleAlgorithm2N
     a::SVector{4, Float64}

src/time_integration/methods_3Sstar.jl

@@ -49,9 +49,9 @@ end
 """
     ParsaniKetchesonDeconinck3Sstar94()
 
-Parsani, Ketcheson, Deconinck (2013)
+- Parsani, Ketcheson, Deconinck (2013)
   Optimized explicit RK schemes for the spectral difference method applied to wave propagation problems
-[DOI: 10.1137/120885899](https://doi.org/10.1137/120885899)
+  [DOI: 10.1137/120885899](https://doi.org/10.1137/120885899)
 """
 struct ParsaniKetchesonDeconinck3Sstar94 <: SimpleAlgorithm3Sstar
     gamma1::SVector{9, Float64}
@@ -100,9 +100,9 @@ end
 """
     ParsaniKetchesonDeconinck3Sstar32()
 
-Parsani, Ketcheson, Deconinck (2013)
+- Parsani, Ketcheson, Deconinck (2013)
   Optimized explicit RK schemes for the spectral difference method applied to wave propagation problems
-[DOI: 10.1137/120885899](https://doi.org/10.1137/120885899)
+  [DOI: 10.1137/120885899](https://doi.org/10.1137/120885899)
 """
 struct ParsaniKetchesonDeconinck3Sstar32 <: SimpleAlgorithm3Sstar
     gamma1::SVector{3, Float64}