WIP: Sc/polytropic 2d wave speed (#1816)

* Added coupling converters.

* Added generic converter_function for structured 2d meshes.

* Added example elixir for coupling converters.

* Cleaned up converter coupling elixir.

* Added equations in coupling converters.

* Added converter  functions.

* Added identity converter function.

* Autoformat for converter coupling implementation.

* Added coupled converter elixir.

* Corrected file name of coupled converters test.

* Removed redundant doc string.

* Added function signature in doc string.

* Removed coverage_override in coupled tests.

* Removed old commented code.

* Update make.jl

Added interface coupling docs to the main menu.

* Update make.jl

Moved converter coupling section.

* Create coupling.md

* Update coupling.md

Added some documentation on coupling converters.

* Removed troublesome AnalysisCallbackCoupled from test.

* Chenged coupling converter function.

* Changed coupling converter function and updated tests.

* Sepcialized coupling function call.

* Removed volume coupling from documentation to avoit confusion.

* Update src/coupling_converters/coupling_converters.jl

Co-authored-by: Hendrik Ranocha <[email protected]>

* Removed redundant converter function for coupling.

* Removed redundant coupling converter file mentioned in some files.

* Autoreformatted.

* Removed old coupled elixir and replaced it with one using converter functions.

* Updated errors for coupled tests.

* Corrected test results for coupled equations.

* Corrected comment.

* Removed coupled test from special tests.

* Removed coupled test from specials.

* Chaned the coupling function to the identity.

* Updated coupling tests.

* Updated errors for coupled test.

* Added advice about binary compatability for coupled equations in the documentation.

* Typo.

* Added numerical fluxes.

* Corrected rs copy routine. Now loop over this semi's components.

* Reformatted equations source file.

* Removed problemating include of time_integration.jl.

* Removed export of deleted methods.

* Reverted to old version of compressible Euler multicomponent with no support for structured grid.

* Renamed documentation file for multi-physics coupling.

* Renamed doc reference.

* Update src/semidiscretization/semidiscretization_coupled.jl

Co-authored-by: Michael Schlottke-Lakemper <[email protected]>

* Update docs/src/multi-physics_coupling.md

Co-authored-by: Michael Schlottke-Lakemper <[email protected]>

* Update docs/src/multi-physics_coupling.md

Co-authored-by: Michael Schlottke-Lakemper <[email protected]>

* Update docs/src/multi-physics_coupling.md

Co-authored-by: Michael Schlottke-Lakemper <[email protected]>

* Reinstated structured_2d_dgsem coupled in special tests.

* Update examples/structured_2d_dgsem/elixir_advection_coupled.jl

Co-authored-by: Michael Schlottke-Lakemper <[email protected]>

* Renamed CouplingFunction to CouplingConverter.

* Update src/semidiscretization/semidiscretization_coupled.jl

Co-authored-by: Michael Schlottke-Lakemper <[email protected]>

* Cleaned the copy of coupled boundary values.

* Reduced time span for example coupling elixir.

* Removed redundant loop.

* Applied formatter.

* Removed default coupling covnerter function.

* Moved coupling converter function into elixir.

* Apply suggestions from code review

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

* Update docs/make.jl

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

* Removed coupling_converters.jl from the include.

* Corrected introduced issue with coupling boundary copy.

The latest change to clean up the boundary copying
introduced a bug related to the determination of the wrong
node indices. This is now corrected.

* Corrected comment on final simulation time.

* Updated errors for coupled test to reflect changed final simulation time.

* Added miladd.

* Corrected coordinate finding in semidiscretization_coupled.

* Fixed issued related to memory allocation.

* Corrected loop over semidiscretization.

* Removed commented out code.

* Fixed type instability with loops over semidiscretizations using
lispy tuple programming.

* Removed obsolete code.

* Fixed another typa instability in coupled semidiscretization.

* Cleaning up of the coupled semidiscretization.

* Autoformatted coupled semidiscretization.

* Fixed last type instability in coupling.

* Autoformatter on semidiscretization.

* Fixed bug in boundary values copy that arose when coupling multiple systems.

* aplpied autoformatter on coupled semidiscretization.

* Extended the structured 2d example elixir for the coupled advection
to 4 semidiscretizations.

This hase two purpuses:
1. Users are given an example fro 2d coupling avoiding common pitfalls.
2. This increases the code coverege for the test.

* Updated test results for coupled advection in 2d to reflect
the 4 semidiscretizations that are now used.

* Added correct errors for tests for the coupled adveciton equations in structured 2d.

* Update examples/structured_2d_dgsem/elixir_advection_coupled.jl

Co-authored-by: Erik Faulhaber <[email protected]>

* Update examples/structured_2d_dgsem/elixir_advection_coupled.jl

Co-authored-by: Erik Faulhaber <[email protected]>

* Update src/semidiscretization/semidiscretization_coupled.jl

Co-authored-by: Erik Faulhaber <[email protected]>

* Update src/semidiscretization/semidiscretization_coupled.jl

Co-authored-by: Erik Faulhaber <[email protected]>

* Update src/semidiscretization/semidiscretization_coupled.jl

Co-authored-by: Erik Faulhaber <[email protected]>

* Update src/semidiscretization/semidiscretization_coupled.jl

Co-authored-by: Erik Faulhaber <[email protected]>

* Update src/semidiscretization/semidiscretization_coupled.jl

Co-authored-by: Erik Faulhaber <[email protected]>

* Update src/semidiscretization/semidiscretization_coupled.jl

Co-authored-by: Erik Faulhaber <[email protected]>

* Update src/semidiscretization/semidiscretization_coupled.jl

Co-authored-by: Erik Faulhaber <[email protected]>

* Corrected foreach_enumerate implementation.

* Fix closing parens

* Remove unused recursive rhs!

* Pass equations to converter function

* Apply formatting

* Reverted copy_to_coupled_boundary to previou version
to avoid type instability.

* Corrected computation of coupled semidiscretizations and fixed memory issue.

* Removed redundant nelements function, as it is no longer used.

* Applied autoformatter.

* Added max_abs_speed_naive( and max_abs_speed_naive for PolytropicEulerEquations2D.

* Reverted coupling elixir to main branch version.
The modified version should be part of a different PR.

* Removed some modified coupling code as this should be part of a different PR.

* Reverted changes on ooupling semidiscretization as this should be part of a different PR.

* Reverted changes partaining the coupling PR.

* Removed changes partaining coupling PR.

* REverted to version including elixir_euler_warm_bubble.jl tests.

* Update src/equations/polytropic_euler_2d.jl

Co-authored-by: Andrew Winters <[email protected]>

* Update src/equations/polytropic_euler_2d.jl

Co-authored-by: Andrew Winters <[email protected]>

* Update src/equations/polytropic_euler_2d.jl

Co-authored-by: Andrew Winters <[email protected]>

* Update src/equations/polytropic_euler_2d.jl

Co-authored-by: Andrés Rueda-Ramírez <[email protected]>

* Update src/equations/polytropic_euler_2d.jl

Co-authored-by: Andrés Rueda-Ramírez <[email protected]>

* Update src/equations/polytropic_euler_2d.jl

Co-authored-by: Daniel Doehring <[email protected]>

* Added consistency and rotation test for LAx-friedrich fluxes for polytropic equations in 2d.

* Applied auto-formatter on polytropic 2d equation.

* Update src/equations/polytropic_euler_2d.jl

Co-authored-by: Andrew Winters <[email protected]>

---------

Co-authored-by: Michael Schlottke-Lakemper <[email protected]>
Co-authored-by: Hendrik Ranocha <[email protected]>
Co-authored-by: Joshua Lampert <[email protected]>
Co-authored-by: Erik Faulhaber <[email protected]>
Co-authored-by: Andrew Winters <[email protected]>
Co-authored-by: Andrés Rueda-Ramírez <[email protected]>
Co-authored-by: Daniel Doehring <[email protected]>
Co-authored-by: iomsn <[email protected]>

src/equations/polytropic_euler_2d.jl

@@ -301,6 +301,46 @@ end
     return abs(v1) + c, abs(v2) + c
 end
 
+# Calculate maximum wave speed for local Lax-Friedrichs-type dissipation as the
+# maximum velocity magnitude plus the maximum speed of sound
+@inline function max_abs_speed_naive(u_ll, u_rr, orientation::Integer,
+                                     equations::PolytropicEulerEquations2D)
+    rho_ll, v1_ll, v2_ll = cons2prim(u_ll, equations)
+    rho_rr, v1_rr, v2_rr = cons2prim(u_rr, equations)
+
+    # Get the velocity value in the appropriate direction
+    if orientation == 1
+        v_ll = v1_ll
+        v_rr = v1_rr
+    else # orientation == 2
+        v_ll = v2_ll
+        v_rr = v2_rr
+    end
+    # Calculate sound speeds (we have p = kappa * rho^gamma)
+    c_ll = sqrt(equations.gamma * equations.kappa * rho_ll^(equations.gamma - 1))
+    c_rr = sqrt(equations.gamma * equations.kappa * rho_rr^(equations.gamma - 1))
+
+    λ_max = max(abs(v_ll), abs(v_rr)) + max(c_ll, c_rr)
+end
+
+@inline function max_abs_speed_naive(u_ll, u_rr, normal_direction::AbstractVector,
+                                     equations::PolytropicEulerEquations2D)
+    rho_ll, v1_ll, v2_ll = cons2prim(u_ll, equations)
+    rho_rr, v1_rr, v2_rr = cons2prim(u_rr, equations)
+
+    # Calculate normal velocities and sound speed (we have p = kappa * rho^gamma)
+    # left
+    v_ll = (v1_ll * normal_direction[1] +
+            v2_ll * normal_direction[2])
+    c_ll = sqrt(equations.gamma * equations.kappa * rho_ll^(equations.gamma - 1))
+    # right
+    v_rr = (v1_rr * normal_direction[1] +
+            v2_rr * normal_direction[2])
+    c_rr = sqrt(equations.gamma * equations.kappa * rho_rr^(equations.gamma - 1))
+
+    return max(abs(v_ll), abs(v_rr)) + max(c_ll, c_rr) * norm(normal_direction)
+end
+
 # Convert conservative variables to primitive
 @inline function cons2prim(u, equations::PolytropicEulerEquations2D)
     rho, rho_v1, rho_v2 = u

test/test_unit.jl

@@ -858,6 +858,30 @@ end
     end
 end
 
+@timed_testset "Consistency check for Lax-Friedrich flux: Polytropic CEE" begin
+    for gamma in [1.4, 1.0, 5 / 3]
+        kappa = 0.5     # Scaling factor for the pressure.
+        equations = PolytropicEulerEquations2D(gamma, kappa)
+        u = SVector(1.1, -0.5, 2.34)
+
+        orientations = [1, 2]
+        for orientation in orientations
+            @test flux_lax_friedrichs(u, u, orientation, equations) ≈
+                  flux(u, orientation, equations)
+        end
+
+        normal_directions = [SVector(1.0, 0.0),
+            SVector(0.0, 1.0),
+            SVector(0.5, -0.5),
+            SVector(-1.2, 0.3)]
+
+        for normal_direction in normal_directions
+            @test flux_lax_friedrichs(u, u, normal_direction, equations) ≈
+                  flux(u, normal_direction, equations)
+        end
+    end
+end
+
 @timed_testset "Consistency check for HLL flux with Davis wave speed estimates: LEE" begin
     flux_hll = FluxHLL(min_max_speed_davis)