add gradient variable type parameter to AbstractEquationsParabolic

docs/literate/src/files/adding_new_parabolic_terms.jl

@@ -18,8 +18,15 @@ equations_hyperbolic = LinearScalarAdvectionEquation2D(advection_velocity);
 # `ConstantAnisotropicDiffusion2D` has a field for `equations_hyperbolic`. It is useful to have
 # information about the hyperbolic system available to the parabolic part so that we can reuse
 # functions defined for hyperbolic equations (such as `varnames`).
-
-struct ConstantAnisotropicDiffusion2D{E, T} <: Trixi.AbstractEquationsParabolic{2, 1}
+#
+# The abstract type `Trixi.AbstractEquationsParabolic` has three parameters: `NDIMS` (the spatial dimension,
+# e.g., 1D, 2D, or 3D), `NVARS` (the number of variables), and `GradientVariable`, which we set as
+# `GradientVariablesConservative`. This indicates that the gradient should be taken with respect to the
+# conservative variables (e.g., the same variables used in `equations_hyperbolic`). Users can also take
+# the gradient with respect to a different set of variables; see, for example, the implementation of
+# [`CompressibleNavierStokesDiffusion2D`](@ref), which can utilize either "primitive" or "entropy" variables.
+
+struct ConstantAnisotropicDiffusion2D{E, T} <: Trixi.AbstractEquationsParabolic{2, 1, GradientVariablesConservative}
   diffusivity::T
   equations_hyperbolic::E
 end

src/Trixi.jl

@@ -152,7 +152,7 @@ export AcousticPerturbationEquations2D,
 export LaplaceDiffusion1D, LaplaceDiffusion2D,
        CompressibleNavierStokesDiffusion2D, CompressibleNavierStokesDiffusion3D
 
-export GradientVariablesPrimitive, GradientVariablesEntropy
+export GradientVariablesConservative, GradientVariablesPrimitive, GradientVariablesEntropy
 
 export flux, flux_central, flux_lax_friedrichs, flux_hll, flux_hllc, flux_hlle,
        flux_godunov,

src/equations/compressible_navier_stokes_2d.jl

@@ -78,7 +78,7 @@ w_2 = \frac{\rho v_1}{p},\, w_3 = \frac{\rho v_2}{p},\, w_4 = -\frac{\rho}{p}
 """
 struct CompressibleNavierStokesDiffusion2D{GradientVariables, RealT <: Real,
                                            E <: AbstractCompressibleEulerEquations{2}} <:
-       AbstractCompressibleNavierStokesDiffusion{2, 4}
+       AbstractCompressibleNavierStokesDiffusion{2, 4, GradientVariables}
     # TODO: parabolic
     # 1) For now save gamma and inv(gamma-1) again, but could potentially reuse them from the Euler equations
     # 2) Add NGRADS as a type parameter here and in AbstractEquationsParabolic, add `ngradients(...)` accessor function
@@ -108,9 +108,6 @@ formulation from
 
 Under `GradientVariablesEntropy`, the Navier-Stokes discretization is provably entropy stable.
 """
-struct GradientVariablesPrimitive end
-struct GradientVariablesEntropy end
-
 # default to primitive gradient variables
 function CompressibleNavierStokesDiffusion2D(equations::CompressibleEulerEquations2D;
                                              mu, Prandtl,

src/equations/compressible_navier_stokes_3d.jl

@@ -78,7 +78,7 @@ w_2 = \frac{\rho v_1}{p},\, w_3 = \frac{\rho v_2}{p},\, w_4 = \frac{\rho v_3}{p}
 """
 struct CompressibleNavierStokesDiffusion3D{GradientVariables, RealT <: Real,
                                            E <: AbstractCompressibleEulerEquations{3}} <:
-       AbstractCompressibleNavierStokesDiffusion{3, 5}
+       AbstractCompressibleNavierStokesDiffusion{3, 5, GradientVariables}
     # TODO: parabolic
     # 1) For now save gamma and inv(gamma-1) again, but could potentially reuse them from the Euler equations
     # 2) Add NGRADS as a type parameter here and in AbstractEquationsParabolic, add `ngradients(...)` accessor function

src/equations/equations.jl

@@ -441,6 +441,6 @@ abstract type AbstractLinearizedEulerEquations{NDIMS, NVARS} <:
               AbstractEquations{NDIMS, NVARS} end
 include("linearized_euler_2d.jl")
 
-abstract type AbstractEquationsParabolic{NDIMS, NVARS} <:
+abstract type AbstractEquationsParabolic{NDIMS, NVARS, GradientVariables} <:
               AbstractEquations{NDIMS, NVARS} end
 end # @muladd

src/equations/equations_parabolic.jl

@@ -2,14 +2,21 @@
 # specialize this function to compute gradients e.g., of primitive variables instead of conservative
 gradient_variable_transformation(::AbstractEquationsParabolic) = cons2cons
 
+# By default, the gradients are taken with respect to the conservative variables.
+# this is reflected by the type parameter `GradientVariablesConservative` in the abstract
+# type `AbstractEquationsParabolic{NDIMS, NVARS, GradientVariablesConservative}`.
+struct GradientVariablesConservative end
+struct GradientVariablesPrimitive end
+struct GradientVariablesEntropy end
+
 # Linear scalar diffusion for use in linear scalar advection-diffusion problems
 abstract type AbstractLaplaceDiffusion{NDIMS, NVARS} <:
-              AbstractEquationsParabolic{NDIMS, NVARS} end
+              AbstractEquationsParabolic{NDIMS, NVARS, GradientVariablesConservative} end
 include("laplace_diffusion_1d.jl")
 include("laplace_diffusion_2d.jl")
 
 # Compressible Navier-Stokes equations
-abstract type AbstractCompressibleNavierStokesDiffusion{NDIMS, NVARS} <:
-              AbstractEquationsParabolic{NDIMS, NVARS} end
+abstract type AbstractCompressibleNavierStokesDiffusion{NDIMS, NVARS, GradientVariables} <:
+              AbstractEquationsParabolic{NDIMS, NVARS, GradientVariables} end
 include("compressible_navier_stokes_2d.jl")
 include("compressible_navier_stokes_3d.jl")