WIP: Sc/mhd treemesh 3d by SimonCan · Pull Request #1323 · trixi-framework/Trixi.jl

SimonCan · 2023-01-10T16:13:04Z

This branch is a fork of the ns-treemesh-3d branch. It implements the compressible visco-resistive MHD equations in 3 dimensions on the treemesh.

This is a todo list before we can merge with the main branch:

Perform tests on different systems, like Alfven waves, Kelvin-Helmholtz suppression and dynamos.
Write tests.
Add at least one more example elixir with source term that captures Ohmic heating. Perhaps a dynamo is a good example for this.

Convergence test for examples/tree_3d_dgsem/elixir_mhd_diffusive_alfven_wave.jl:

####################################################################################################
l2
rho                 rho_v1              rho_v2              rho_v3              rho_e_total         B1                  B2                  B3                  psi                 
error     EOC       error     EOC       error     EOC       error     EOC       error     EOC       error     EOC       error     EOC       error     EOC       error     EOC       
2.82e-05  -         2.54e-05  -         1.23e-05  -         2.86e-05  -         1.52e-05  -         2.61e-05  -         1.23e-05  -         2.86e-05  -         3.45e-06  -         
1.82e-06  3.95      1.77e-06  3.84      8.30e-07  3.88      2.00e-06  3.84      1.77e-06  3.10      1.89e-06  3.79      7.68e-07  4.00      1.98e-06  3.85      4.08e-07  3.08      
1.20e-07  3.92      2.81e-07  2.66      1.37e-07  2.60      3.15e-07  2.66      1.92e-07  3.20      1.53e-07  3.62      4.32e-08  4.15      1.52e-07  3.71      4.87e-08  3.07      

mean      3.94      mean      3.25      mean      3.24      mean      3.25      mean      3.15      mean      3.71      mean      4.08      mean      3.78      mean      3.07      
----------------------------------------------------------------------------------------------------
linf
rho                 rho_v1              rho_v2              rho_v3              rho_e_total         B1                  B2                  B3                  psi                 
error     EOC       error     EOC       error     EOC       error     EOC       error     EOC       error     EOC       error     EOC       error     EOC       error     EOC       
6.44e-05  -         5.54e-05  -         2.70e-05  -         6.21e-05  -         6.13e-05  -         5.50e-05  -         2.91e-05  -         6.22e-05  -         1.20e-05  -         
4.18e-06  3.94      3.76e-06  3.88      1.98e-06  3.77      4.39e-06  3.82      6.16e-06  3.31      4.05e-06  3.76      1.88e-06  3.95      4.00e-06  3.96      1.16e-06  3.37      
2.56e-07  4.03      6.51e-07  2.53      3.85e-07  2.36      6.78e-07  2.70      6.24e-07  3.30      3.94e-07  3.36      1.21e-07  3.96      3.91e-07  3.36      1.10e-07  3.39      

mean      3.99      mean      3.21      mean      3.07      mean      3.26      mean      3.31      mean      3.56      mean      3.95      mean      3.66      mean      3.38      
----------------------------------------------------------------------------------------------------
(Dict(:l2 => [3.952415644889589 3.844680905098259 … 3.850140750933816 3.078559686325443; 3.9227371835038847 2.656199757465629 … 3.7083121872841254 3.068010438713628], :linf => [3.9449368370829605 3.883093769494825 … 3.960055037764503 3.3737554866850537; 4.032403421597966 2.529517445602747 … 3.356307225358875 3.3946538077719426]), Dict{Symbol, LinearAlgebra.Transpose{Float64, Matrix{Float64}}}(:l2 => [2.8186561413297704e-5 2.5427812774320658e-5 … 2.8594041808694996e-5 3.4469864312446496e-6; 1.8207337115709807e-6 1.769883697062282e-6 … 1.9827487935071304e-6 4.080381452736118e-7; 1.2005627824705508e-7 2.807688527216588e-7 … 1.5168914122661963e-7 4.8656133653046794e-8], :linf => [6.439065779950681e-5 5.5417382982404784e-5 … 6.224485633657059e-5 1.2003505640157272e-5; 4.18098435839287e-6 3.755937114800073e-6 … 3.999522258095467e-6 1.1579945124350865e-6; 2.5550779747529617e-7 6.5051555626916e-7 … 3.9053410692477253e-7 1.101067338920899e-7]))

…onvergence testing

…into ns-treemesh-3d

forgot the return statement

Conflicts: src/callbacks_step/analysis_dgmulti.jl

Co-authored-by: Hendrik Ranocha <ranocha@users.noreply.github.com>

…vergence test.

SimonCan · 2024-02-16T18:21:14Z

Corrected the convergence tests. Seems to have improved the convergence rate.

…umbers.

…c) pass. Add periodicity = True, as it is not default anymore. Make SemidiscretizationHyperbolicParabolic mutable.

…rk/Trixi.jl into sc/mhd-treemesh-3d

github-actions · 2026-04-29T17:08:38Z

+    r_1 = 0.02*sqrt(5)*pi*sin(-sqrt(5)*pi*t + pi*(x[1] + 2*x[2] - 3.0) + 1)
+
+    r_2 = sqrt(5)*pi^2*mu_const*(-0.04*(0.02*cos(-sqrt(5)*pi*t + pi*(x[1] + 2*x[2] - 3.0) + 1) + 1)^2*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0)) + (0.02*cos(-sqrt(5)*pi*t + pi*(x[1] + 2*x[2] - 3.0) + 1) + 1)*(0.0012*cos(-2*sqrt(5)*pi*t + 2*pi*x[1] + 4*pi*x[2] + 1) - 0.0004*cos(1)) + 3.2e-5*sin(-sqrt(5)*pi*t + pi*(x[1] + 2*x[2] - 3.0) + 1)^2*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0)))/(0.02*cos(-sqrt(5)*pi*t + pi*(x[1] + 2*x[2] - 3.0) + 1) + 1)^3
+
+    r_3 = -sqrt(5)*pi^2*mu_const*(-0.02*(0.02*cos(-sqrt(5)*pi*t + pi*(x[1] + 2*x[2] - 3.0) + 1) + 1)^2*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0)) + (0.02*cos(-sqrt(5)*pi*t + pi*(x[1] + 2*x[2] - 3.0) + 1) + 1)*(0.0006*cos(-2*sqrt(5)*pi*t + 2*pi*x[1] + 4*pi*x[2] + 1) - 0.0002*cos(1)) + 1.6e-5*sin(-sqrt(5)*pi*t + pi*(x[1] + 2*x[2] - 3.0) + 1)^2*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0)))/(0.02*cos(-sqrt(5)*pi*t + pi*(x[1] + 2*x[2] - 3.0) + 1) + 1)^3
+
+    r_4 = -pi^2*mu_const*((0.003*sin(-2*sqrt(5)*pi*t + 2*pi*x[1] + 4*pi*x[2] + 1) + 0.001*sin(1))*(0.02*cos(-sqrt(5)*pi*t + pi*(x[1] + 2*x[2] - 3.0) + 1) + 1) + 0.1*(0.02*cos(-sqrt(5)*pi*t + pi*(x[1] + 2*x[2] - 3.0) + 1) + 1)^2*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2])) - 8.0e-5*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))*sin(-sqrt(5)*pi*t + pi*(x[1] + 2*x[2] - 3.0) + 1)^2)/(0.02*cos(-sqrt(5)*pi*t + pi*(x[1] + 2*x[2] - 3.0) + 1) + 1)^3
+
+#     r_5 = 0.2*pi*(2.77777777777778e-7*pi*mu_const*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))^2*sin(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1) -2.58888888888889e-5*pi*mu_const*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))^2*sin(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^2 + 1.38888888888889e-7*pi*mu_const*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^3 - 1.78888888888889e-5*pi*mu_const*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^2 + 0.000547222222222222*pi*mu_const*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1) + 2.77777777777778e-7*pi*mu_const*sin(-sqrt(5)*pi*t +pi*x[1] + 2*pi*x[2] + 1)^2*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1) - 2.58888888888889e-5*pi*mu_const*sin(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^2*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0))^2 + 1.38888888888889e-7*pi*mu_const*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^3 - 1.78888888888889e-5*pi*mu_const*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^2 + 0.000547222222222223*pi*mu_const*cos(pi*(sqrt(5)*t - x[1] -2*x[2] + 3.0))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1) + 1.0e-7*sqrt(5)*(-sin(-4*sqrt(5)*pi*t + 4*pi*x[1] + 8*pi*x[2] + 2) + 2*sin(-2*sqrt(5)*pi*t + 2*pi*x[1] + 4*pi*x[2] + 2) - sin(2)) + 1.0e-7*sqrt(5)*(sin(-4*sqrt(5)*pi*t + 4*pi*x[1] + 8*pi*x[2] + 2) + 2*sin(-2*sqrt(5)*pi*t + 2*pi*x[1] + 4*pi*x[2] + 2) + sin(2)) - 8.0e-9*sqrt(5)*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))^2*sin(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^2 - 2.0e-5*sqrt(5)*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))^2*sin(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1) - 8.0e-9*sqrt(5)*sin(-sqrt(5)*pi*t+ pi*x[1] + 2*pi*x[2] + 1)*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^2 - 2.0e-5*sqrt(5)*sin(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0))^2)/(-0.04*sin(pi*x[2])*sin(-sqrt(5)*pi*t + pi*x[1] + pi*x[2] + 1) + 0.02*cos(-sqrt(5)*pi*t + pi*x[1] + 1) - 1.0)^4
+
+    r_5 = 0.2*pi*(1.7205356741103e-21*pi*mu_const*(cos(-4*sqrt(5)*pi*t + 4*pi*x[1] + 8*pi*x[2] + 2) - cos(2)) - 1.01643953670516e-19*pi*mu_const*(cos(-3*sqrt(5)*pi*t + 3*pi*x[1] + 6*pi*x[2] + 1) - cos(sqrt(5)*pi*t - pi*x[1] - 2*pi*x[2] + 1)) + 2.77777777777778e-7*pi*mu_const*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))^2*sin(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1) - 2.58888888888889e-5*pi*mu_const*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))^2*sin(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^2 + 1.38888888888889e-7*pi*mu_const*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^3 - 1.78888888888889e-5*pi*mu_const*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^2 + 0.000547222222222222*pi*mu_const*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1) + 4.33680868994202e-18*pi*mu_const*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))^2 - 1.17643464896431e-22*pi*mu_const*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))*sin(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0))*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^2 + 2.77777777777778e-7*pi*mu_const*sin(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^2*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1) - 2.58888888888889e-5*pi*mu_const*sin(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^2*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0))^2 - 2.16840434497101e-25*pi*mu_const*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^4 + 1.38888888888889e-7*pi*mu_const*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^3 - 1.78888888888889e-5*pi*mu_const*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^2 + 0.000547222222222223*pi*mu_const*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1) - 6.64073830647371e-18*pi*mu_const*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0))^2 + 1.0842021724855e-21*sqrt(5)*(-sin(-3*sqrt(5)*pi*t + 3*pi*x[1] + 6*pi*x[2] + 1) + sin(sqrt(5)*pi*t - pi*x[1] - 2*pi*x[2] + 1)) + 1.0842021724855e-27*sqrt(5)*(cos(-2*sqrt(5)*pi*t + 2*pi*x[1] + 4*pi*x[2] + 2) + 1)^2*sin(pi*(-2*sqrt(5)*t + 2*x[1] + 4*x[2])) - 1.62630325872826e-23*sqrt(5)*(-2*sin(pi*(-2*sqrt(5)*t + 2*x[1] + 4*x[2])) - sin(-4*sqrt(5)*pi*t + 4*pi*x[1] + 8*pi*x[2] + 2) + sin(2)) + 1.0e-7*sqrt(5)*(-sin(-4*sqrt(5)*pi*t + 4*pi*x[1] + 8*pi*x[2] + 2) + 2*sin(-2*sqrt(5)*pi*t + 2*pi*x[1] + 4*pi*x[2] + 2) - sin(2)) + 1.0e-7*sqrt(5)*(sin(-4*sqrt(5)*pi*t + 4*pi*x[1] + 8*pi*x[2] + 2) + 2*sin(-2*sqrt(5)*pi*t + 2*pi*x[1] + 4*pi*x[2] + 2) + sin(2)) + 2.71050543121376e-20*sqrt(5)*sin(pi*(-2*sqrt(5)*t + 2*x[1] + 4*x[2])) - 8.0e-9*sqrt(5)*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))^2*sin(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^2 - 2.0e-5*sqrt(5)*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))^2*sin(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1) + 1.73472347597681e-24*sqrt(5)*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0))*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^3 - 8.0e-9*sqrt(5)*sin(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^2 - 2.0e-5*sqrt(5)*sin(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0))^2)/(-0.04*sin(pi*x[2])*sin(-sqrt(5)*pi*t + pi*x[1] + pi*x[2] + 1) + 0.02*cos(-sqrt(5)*pi*t + pi*x[1] + 1) - 1.0)^4
+
+    r_6 = pi*(-0.04*(sqrt(5)*pi*eta_const*cos(pi*(-sqrt(5)*t + x[1] + 2*x[2])) + sin(pi*(-sqrt(5)*t + x[1] + 2*x[2])))*(0.02*cos(-sqrt(5)*pi*t + pi*(x[1] + 2*x[2] - 3.0) + 1) + 1)^2 + 0.04*(0.02*cos(-sqrt(5)*pi*t + pi*(x[1] + 2*x[2] - 3.0) + 1) + 1)*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2])) + 0.0004*sin(-2*sqrt(5)*pi*t + 2*pi*x[1] + 4*pi*x[2] + 1) + 0.0004*sin(1))/(0.02*cos(-sqrt(5)*pi*t + pi*(x[1] + 2*x[2] - 3.0) + 1) + 1)^2
+
+    r_7 = pi*(0.02*(sqrt(5)*pi*eta_const*cos(pi*(-sqrt(5)*t + x[1] + 2*x[2])) + sin(pi*(-sqrt(5)*t + x[1] + 2*x[2])))*(0.02*cos(-sqrt(5)*pi*t + pi*(x[1] + 2*x[2] - 3.0) + 1) + 1)^2 - 0.02*(0.02*cos(-sqrt(5)*pi*t + pi*(x[1] + 2*x[2] - 3.0) + 1) + 1)*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2])) - 0.0002*sin(-2*sqrt(5)*pi*t + 2*pi*x[1] + 4*pi*x[2] + 1) - 0.0002*sin(1))/(0.02*cos(-sqrt(5)*pi*t + pi*(x[1]+ 2*x[2] - 3.0) + 1) + 1)^2
+
+    r_8 = pi*((0.1*pi*eta_const*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2])) + 0.02*sqrt(5)*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0)))*(0.02*cos(-sqrt(5)*pi*t + pi*(x[1] + 2*x[2] - 3.0) + 1) + 1)^2 - 0.02*sqrt(5)*(0.02*cos(-sqrt(5)*pi*t + pi*(x[1] + 2*x[2] - 3.0) + 1) +1)*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0)) + 0.0002*sqrt(5)*(cos(-2*sqrt(5)*pi*t + 2*pi*x[1] + 4*pi*x[2] + 1) - cos(1)))/(0.02*cos(-sqrt(5)*pi*t + pi*(x[1] + 2*x[2] - 3.0) + 1) + 1)^2


[JuliaFormatter] _{reported by reviewdog 🐶}

Suggested change

r_1 = 0.02*sqrt(5)*pi*sin(-sqrt(5)*pi*t + pi*(x[1] + 2*x[2] - 3.0) + 1)

r_2 = sqrt(5)*pi^2*mu_const*(-0.04*(0.02*cos(-sqrt(5)*pi*t + pi*(x[1] + 2*x[2] - 3.0) + 1) + 1)^2*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0)) + (0.02*cos(-sqrt(5)*pi*t + pi*(x[1] + 2*x[2] - 3.0) + 1) + 1)*(0.0012*cos(-2*sqrt(5)*pi*t + 2*pi*x[1] + 4*pi*x[2] + 1) - 0.0004*cos(1)) + 3.2e-5*sin(-sqrt(5)*pi*t + pi*(x[1] + 2*x[2] - 3.0) + 1)^2*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0)))/(0.02*cos(-sqrt(5)*pi*t + pi*(x[1] + 2*x[2] - 3.0) + 1) + 1)^3

r_3 = -sqrt(5)*pi^2*mu_const*(-0.02*(0.02*cos(-sqrt(5)*pi*t + pi*(x[1] + 2*x[2] - 3.0) + 1) + 1)^2*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0)) + (0.02*cos(-sqrt(5)*pi*t + pi*(x[1] + 2*x[2] - 3.0) + 1) + 1)*(0.0006*cos(-2*sqrt(5)*pi*t + 2*pi*x[1] + 4*pi*x[2] + 1) - 0.0002*cos(1)) + 1.6e-5*sin(-sqrt(5)*pi*t + pi*(x[1] + 2*x[2] - 3.0) + 1)^2*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0)))/(0.02*cos(-sqrt(5)*pi*t + pi*(x[1] + 2*x[2] - 3.0) + 1) + 1)^3

r_4 = -pi^2*mu_const*((0.003*sin(-2*sqrt(5)*pi*t + 2*pi*x[1] + 4*pi*x[2] + 1) + 0.001*sin(1))*(0.02*cos(-sqrt(5)*pi*t + pi*(x[1] + 2*x[2] - 3.0) + 1) + 1) + 0.1*(0.02*cos(-sqrt(5)*pi*t + pi*(x[1] + 2*x[2] - 3.0) + 1) + 1)^2*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2])) - 8.0e-5*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))*sin(-sqrt(5)*pi*t + pi*(x[1] + 2*x[2] - 3.0) + 1)^2)/(0.02*cos(-sqrt(5)*pi*t + pi*(x[1] + 2*x[2] - 3.0) + 1) + 1)^3

# r_5 = 0.2*pi*(2.77777777777778e-7*pi*mu_const*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))^2*sin(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1) -2.58888888888889e-5*pi*mu_const*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))^2*sin(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^2 + 1.38888888888889e-7*pi*mu_const*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^3 - 1.78888888888889e-5*pi*mu_const*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^2 + 0.000547222222222222*pi*mu_const*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1) + 2.77777777777778e-7*pi*mu_const*sin(-sqrt(5)*pi*t +pi*x[1] + 2*pi*x[2] + 1)^2*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1) - 2.58888888888889e-5*pi*mu_const*sin(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^2*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0))^2 + 1.38888888888889e-7*pi*mu_const*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^3 - 1.78888888888889e-5*pi*mu_const*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^2 + 0.000547222222222223*pi*mu_const*cos(pi*(sqrt(5)*t - x[1] -2*x[2] + 3.0))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1) + 1.0e-7*sqrt(5)*(-sin(-4*sqrt(5)*pi*t + 4*pi*x[1] + 8*pi*x[2] + 2) + 2*sin(-2*sqrt(5)*pi*t + 2*pi*x[1] + 4*pi*x[2] + 2) - sin(2)) + 1.0e-7*sqrt(5)*(sin(-4*sqrt(5)*pi*t + 4*pi*x[1] + 8*pi*x[2] + 2) + 2*sin(-2*sqrt(5)*pi*t + 2*pi*x[1] + 4*pi*x[2] + 2) + sin(2)) - 8.0e-9*sqrt(5)*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))^2*sin(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^2 - 2.0e-5*sqrt(5)*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))^2*sin(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1) - 8.0e-9*sqrt(5)*sin(-sqrt(5)*pi*t+ pi*x[1] + 2*pi*x[2] + 1)*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^2 - 2.0e-5*sqrt(5)*sin(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0))^2)/(-0.04*sin(pi*x[2])*sin(-sqrt(5)*pi*t + pi*x[1] + pi*x[2] + 1) + 0.02*cos(-sqrt(5)*pi*t + pi*x[1] + 1) - 1.0)^4

r_5 = 0.2*pi*(1.7205356741103e-21*pi*mu_const*(cos(-4*sqrt(5)*pi*t + 4*pi*x[1] + 8*pi*x[2] + 2) - cos(2)) - 1.01643953670516e-19*pi*mu_const*(cos(-3*sqrt(5)*pi*t + 3*pi*x[1] + 6*pi*x[2] + 1) - cos(sqrt(5)*pi*t - pi*x[1] - 2*pi*x[2] + 1)) + 2.77777777777778e-7*pi*mu_const*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))^2*sin(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1) - 2.58888888888889e-5*pi*mu_const*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))^2*sin(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^2 + 1.38888888888889e-7*pi*mu_const*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^3 - 1.78888888888889e-5*pi*mu_const*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^2 + 0.000547222222222222*pi*mu_const*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1) + 4.33680868994202e-18*pi*mu_const*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))^2 - 1.17643464896431e-22*pi*mu_const*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))*sin(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0))*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^2 + 2.77777777777778e-7*pi*mu_const*sin(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^2*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1) - 2.58888888888889e-5*pi*mu_const*sin(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^2*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0))^2 - 2.16840434497101e-25*pi*mu_const*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^4 + 1.38888888888889e-7*pi*mu_const*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^3 - 1.78888888888889e-5*pi*mu_const*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^2 + 0.000547222222222223*pi*mu_const*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1) - 6.64073830647371e-18*pi*mu_const*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0))^2 + 1.0842021724855e-21*sqrt(5)*(-sin(-3*sqrt(5)*pi*t + 3*pi*x[1] + 6*pi*x[2] + 1) + sin(sqrt(5)*pi*t - pi*x[1] - 2*pi*x[2] + 1)) + 1.0842021724855e-27*sqrt(5)*(cos(-2*sqrt(5)*pi*t + 2*pi*x[1] + 4*pi*x[2] + 2) + 1)^2*sin(pi*(-2*sqrt(5)*t + 2*x[1] + 4*x[2])) - 1.62630325872826e-23*sqrt(5)*(-2*sin(pi*(-2*sqrt(5)*t + 2*x[1] + 4*x[2])) - sin(-4*sqrt(5)*pi*t + 4*pi*x[1] + 8*pi*x[2] + 2) + sin(2)) + 1.0e-7*sqrt(5)*(-sin(-4*sqrt(5)*pi*t + 4*pi*x[1] + 8*pi*x[2] + 2) + 2*sin(-2*sqrt(5)*pi*t + 2*pi*x[1] + 4*pi*x[2] + 2) - sin(2)) + 1.0e-7*sqrt(5)*(sin(-4*sqrt(5)*pi*t + 4*pi*x[1] + 8*pi*x[2] + 2) + 2*sin(-2*sqrt(5)*pi*t + 2*pi*x[1] + 4*pi*x[2] + 2) + sin(2)) + 2.71050543121376e-20*sqrt(5)*sin(pi*(-2*sqrt(5)*t + 2*x[1] + 4*x[2])) - 8.0e-9*sqrt(5)*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))^2*sin(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^2 - 2.0e-5*sqrt(5)*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))^2*sin(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1) + 1.73472347597681e-24*sqrt(5)*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0))*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^3 - 8.0e-9*sqrt(5)*sin(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^2 - 2.0e-5*sqrt(5)*sin(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0))^2)/(-0.04*sin(pi*x[2])*sin(-sqrt(5)*pi*t + pi*x[1] + pi*x[2] + 1) + 0.02*cos(-sqrt(5)*pi*t + pi*x[1] + 1) - 1.0)^4

r_6 = pi*(-0.04*(sqrt(5)*pi*eta_const*cos(pi*(-sqrt(5)*t + x[1] + 2*x[2])) + sin(pi*(-sqrt(5)*t + x[1] + 2*x[2])))*(0.02*cos(-sqrt(5)*pi*t + pi*(x[1] + 2*x[2] - 3.0) + 1) + 1)^2 + 0.04*(0.02*cos(-sqrt(5)*pi*t + pi*(x[1] + 2*x[2] - 3.0) + 1) + 1)*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2])) + 0.0004*sin(-2*sqrt(5)*pi*t + 2*pi*x[1] + 4*pi*x[2] + 1) + 0.0004*sin(1))/(0.02*cos(-sqrt(5)*pi*t + pi*(x[1] + 2*x[2] - 3.0) + 1) + 1)^2

r_7 = pi*(0.02*(sqrt(5)*pi*eta_const*cos(pi*(-sqrt(5)*t + x[1] + 2*x[2])) + sin(pi*(-sqrt(5)*t + x[1] + 2*x[2])))*(0.02*cos(-sqrt(5)*pi*t + pi*(x[1] + 2*x[2] - 3.0) + 1) + 1)^2 - 0.02*(0.02*cos(-sqrt(5)*pi*t + pi*(x[1] + 2*x[2] - 3.0) + 1) + 1)*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2])) - 0.0002*sin(-2*sqrt(5)*pi*t + 2*pi*x[1] + 4*pi*x[2] + 1) - 0.0002*sin(1))/(0.02*cos(-sqrt(5)*pi*t + pi*(x[1]+ 2*x[2] - 3.0) + 1) + 1)^2

r_8 = pi*((0.1*pi*eta_const*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2])) + 0.02*sqrt(5)*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0)))*(0.02*cos(-sqrt(5)*pi*t + pi*(x[1] + 2*x[2] - 3.0) + 1) + 1)^2 - 0.02*sqrt(5)*(0.02*cos(-sqrt(5)*pi*t + pi*(x[1] + 2*x[2] - 3.0) + 1) +1)*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0)) + 0.0002*sqrt(5)*(cos(-2*sqrt(5)*pi*t + 2*pi*x[1] + 4*pi*x[2] + 1) - cos(1)))/(0.02*cos(-sqrt(5)*pi*t + pi*(x[1] + 2*x[2] - 3.0) + 1) + 1)^2

r_1 = 0.02 * sqrt(5) * pi * sin(-sqrt(5) * pi * t + pi * (x[1] + 2 * x[2] - 3.0) + 1)

r_2 = sqrt(5) * pi^2 * mu_const *

(-0.04 *

(0.02 * cos(-sqrt(5) * pi * t + pi * (x[1] + 2 * x[2] - 3.0) + 1) + 1)^2 *

cos(pi * (sqrt(5) * t - x[1] - 2 * x[2] + 3.0)) +

(0.02 * cos(-sqrt(5) * pi * t + pi * (x[1] + 2 * x[2] - 3.0) + 1) + 1) *

(0.0012 * cos(-2 * sqrt(5) * pi * t + 2 * pi * x[1] + 4 * pi * x[2] + 1) -

0.0004 * cos(1)) +

3.2e-5 * sin(-sqrt(5) * pi * t + pi * (x[1] + 2 * x[2] - 3.0) + 1)^2 *

cos(pi * (sqrt(5) * t - x[1] - 2 * x[2] + 3.0))) /

(0.02 * cos(-sqrt(5) * pi * t + pi * (x[1] + 2 * x[2] - 3.0) + 1) + 1)^3

r_3 = -sqrt(5) * pi^2 * mu_const *

(-0.02 *

(0.02 * cos(-sqrt(5) * pi * t + pi * (x[1] + 2 * x[2] - 3.0) + 1) + 1)^2 *

cos(pi * (sqrt(5) * t - x[1] - 2 * x[2] + 3.0)) +

(0.02 * cos(-sqrt(5) * pi * t + pi * (x[1] + 2 * x[2] - 3.0) + 1) + 1) *

(0.0006 * cos(-2 * sqrt(5) * pi * t + 2 * pi * x[1] + 4 * pi * x[2] + 1) -

0.0002 * cos(1)) +

1.6e-5 * sin(-sqrt(5) * pi * t + pi * (x[1] + 2 * x[2] - 3.0) + 1)^2 *

cos(pi * (sqrt(5) * t - x[1] - 2 * x[2] + 3.0))) /

(0.02 * cos(-sqrt(5) * pi * t + pi * (x[1] + 2 * x[2] - 3.0) + 1) + 1)^3

r_4 = -pi^2 * mu_const *

((0.003 * sin(-2 * sqrt(5) * pi * t + 2 * pi * x[1] + 4 * pi * x[2] + 1) +

0.001 * sin(1)) *

(0.02 * cos(-sqrt(5) * pi * t + pi * (x[1] + 2 * x[2] - 3.0) + 1) + 1) +

0.1 * (0.02 * cos(-sqrt(5) * pi * t + pi * (x[1] + 2 * x[2] - 3.0) + 1) + 1)^2 *

sin(pi * (-sqrt(5) * t + x[1] + 2 * x[2])) -

8.0e-5 * sin(pi * (-sqrt(5) * t + x[1] + 2 * x[2])) *

sin(-sqrt(5) * pi * t + pi * (x[1] + 2 * x[2] - 3.0) + 1)^2) /

(0.02 * cos(-sqrt(5) * pi * t + pi * (x[1] + 2 * x[2] - 3.0) + 1) + 1)^3

# r_5 = 0.2*pi*(2.77777777777778e-7*pi*mu_const*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))^2*sin(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1) -2.58888888888889e-5*pi*mu_const*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))^2*sin(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^2 + 1.38888888888889e-7*pi*mu_const*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^3 - 1.78888888888889e-5*pi*mu_const*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^2 + 0.000547222222222222*pi*mu_const*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1) + 2.77777777777778e-7*pi*mu_const*sin(-sqrt(5)*pi*t +pi*x[1] + 2*pi*x[2] + 1)^2*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1) - 2.58888888888889e-5*pi*mu_const*sin(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^2*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0))^2 + 1.38888888888889e-7*pi*mu_const*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^3 - 1.78888888888889e-5*pi*mu_const*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^2 + 0.000547222222222223*pi*mu_const*cos(pi*(sqrt(5)*t - x[1] -2*x[2] + 3.0))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1) + 1.0e-7*sqrt(5)*(-sin(-4*sqrt(5)*pi*t + 4*pi*x[1] + 8*pi*x[2] + 2) + 2*sin(-2*sqrt(5)*pi*t + 2*pi*x[1] + 4*pi*x[2] + 2) - sin(2)) + 1.0e-7*sqrt(5)*(sin(-4*sqrt(5)*pi*t + 4*pi*x[1] + 8*pi*x[2] + 2) + 2*sin(-2*sqrt(5)*pi*t + 2*pi*x[1] + 4*pi*x[2] + 2) + sin(2)) - 8.0e-9*sqrt(5)*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))^2*sin(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^2 - 2.0e-5*sqrt(5)*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))^2*sin(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1) - 8.0e-9*sqrt(5)*sin(-sqrt(5)*pi*t+ pi*x[1] + 2*pi*x[2] + 1)*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^2 - 2.0e-5*sqrt(5)*sin(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0))^2)/(-0.04*sin(pi*x[2])*sin(-sqrt(5)*pi*t + pi*x[1] + pi*x[2] + 1) + 0.02*cos(-sqrt(5)*pi*t + pi*x[1] + 1) - 1.0)^4

r_5 = 0.2 * pi *

(1.7205356741103e-21 * pi * mu_const *

(cos(-4 * sqrt(5) * pi * t + 4 * pi * x[1] + 8 * pi * x[2] + 2) - cos(2)) -

1.01643953670516e-19 * pi * mu_const *

(cos(-3 * sqrt(5) * pi * t + 3 * pi * x[1] + 6 * pi * x[2] + 1) -

cos(sqrt(5) * pi * t - pi * x[1] - 2 * pi * x[2] + 1)) +

2.77777777777778e-7 * pi * mu_const *

sin(pi * (-sqrt(5) * t + x[1] + 2 * x[2]))^2 *

sin(-sqrt(5) * pi * t + pi * x[1] + 2 * pi * x[2] + 1)^2 *

cos(-sqrt(5) * pi * t + pi * x[1] + 2 * pi * x[2] + 1) -

2.58888888888889e-5 * pi * mu_const *

sin(pi * (-sqrt(5) * t + x[1] + 2 * x[2]))^2 *

sin(-sqrt(5) * pi * t + pi * x[1] + 2 * pi * x[2] + 1)^2 +

1.38888888888889e-7 * pi * mu_const *

sin(pi * (-sqrt(5) * t + x[1] + 2 * x[2]))^2 *

cos(-sqrt(5) * pi * t + pi * x[1] + 2 * pi * x[2] + 1)^3 -

1.78888888888889e-5 * pi * mu_const *

sin(pi * (-sqrt(5) * t + x[1] + 2 * x[2]))^2 *

cos(-sqrt(5) * pi * t + pi * x[1] + 2 * pi * x[2] + 1)^2 +

0.000547222222222222 * pi * mu_const *

sin(pi * (-sqrt(5) * t + x[1] + 2 * x[2]))^2 *

cos(-sqrt(5) * pi * t + pi * x[1] + 2 * pi * x[2] + 1) +

4.33680868994202e-18 * pi * mu_const *

sin(pi * (-sqrt(5) * t + x[1] + 2 * x[2]))^2 -

1.17643464896431e-22 * pi * mu_const *

sin(pi * (-sqrt(5) * t + x[1] + 2 * x[2])) *

sin(-sqrt(5) * pi * t + pi * x[1] + 2 * pi * x[2] + 1) *

cos(pi * (sqrt(5) * t - x[1] - 2 * x[2] + 3.0)) *

cos(-sqrt(5) * pi * t + pi * x[1] + 2 * pi * x[2] + 1)^2 +

2.77777777777778e-7 * pi * mu_const *

sin(-sqrt(5) * pi * t + pi * x[1] + 2 * pi * x[2] + 1)^2 *

cos(pi * (sqrt(5) * t - x[1] - 2 * x[2] + 3.0))^2 *

cos(-sqrt(5) * pi * t + pi * x[1] + 2 * pi * x[2] + 1) -

2.58888888888889e-5 * pi * mu_const *

sin(-sqrt(5) * pi * t + pi * x[1] + 2 * pi * x[2] + 1)^2 *

cos(pi * (sqrt(5) * t - x[1] - 2 * x[2] + 3.0))^2 -

2.16840434497101e-25 * pi * mu_const *

cos(pi * (sqrt(5) * t - x[1] - 2 * x[2] + 3.0))^2 *

cos(-sqrt(5) * pi * t + pi * x[1] + 2 * pi * x[2] + 1)^4 +

1.38888888888889e-7 * pi * mu_const *

cos(pi * (sqrt(5) * t - x[1] - 2 * x[2] + 3.0))^2 *

cos(-sqrt(5) * pi * t + pi * x[1] + 2 * pi * x[2] + 1)^3 -

1.78888888888889e-5 * pi * mu_const *

cos(pi * (sqrt(5) * t - x[1] - 2 * x[2] + 3.0))^2 *

cos(-sqrt(5) * pi * t + pi * x[1] + 2 * pi * x[2] + 1)^2 +

0.000547222222222223 * pi * mu_const *

cos(pi * (sqrt(5) * t - x[1] - 2 * x[2] + 3.0))^2 *

cos(-sqrt(5) * pi * t + pi * x[1] + 2 * pi * x[2] + 1) -

6.64073830647371e-18 * pi * mu_const *

cos(pi * (sqrt(5) * t - x[1] - 2 * x[2] + 3.0))^2 +

1.0842021724855e-21 * sqrt(5) *

(-sin(-3 * sqrt(5) * pi * t + 3 * pi * x[1] + 6 * pi * x[2] + 1) +

sin(sqrt(5) * pi * t - pi * x[1] - 2 * pi * x[2] + 1)) +

1.0842021724855e-27 * sqrt(5) *

(cos(-2 * sqrt(5) * pi * t + 2 * pi * x[1] + 4 * pi * x[2] + 2) + 1)^2 *

sin(pi * (-2 * sqrt(5) * t + 2 * x[1] + 4 * x[2])) -

1.62630325872826e-23 * sqrt(5) *

(-2 * sin(pi * (-2 * sqrt(5) * t + 2 * x[1] + 4 * x[2])) -

sin(-4 * sqrt(5) * pi * t + 4 * pi * x[1] + 8 * pi * x[2] + 2) + sin(2)) +

1.0e-7 * sqrt(5) *

(-sin(-4 * sqrt(5) * pi * t + 4 * pi * x[1] + 8 * pi * x[2] + 2) +

2 * sin(-2 * sqrt(5) * pi * t + 2 * pi * x[1] + 4 * pi * x[2] + 2) - sin(2)) +

1.0e-7 * sqrt(5) *

(sin(-4 * sqrt(5) * pi * t + 4 * pi * x[1] + 8 * pi * x[2] + 2) +

2 * sin(-2 * sqrt(5) * pi * t + 2 * pi * x[1] + 4 * pi * x[2] + 2) + sin(2)) +

2.71050543121376e-20 * sqrt(5) *

sin(pi * (-2 * sqrt(5) * t + 2 * x[1] + 4 * x[2])) -

8.0e-9 * sqrt(5) * sin(pi * (-sqrt(5) * t + x[1] + 2 * x[2]))^2 *

sin(-sqrt(5) * pi * t + pi * x[1] + 2 * pi * x[2] + 1) *

cos(-sqrt(5) * pi * t + pi * x[1] + 2 * pi * x[2] + 1)^2 -

2.0e-5 * sqrt(5) * sin(pi * (-sqrt(5) * t + x[1] + 2 * x[2]))^2 *

sin(-sqrt(5) * pi * t + pi * x[1] + 2 * pi * x[2] + 1) +

1.73472347597681e-24 * sqrt(5) * sin(pi * (-sqrt(5) * t + x[1] + 2 * x[2])) *

cos(pi * (sqrt(5) * t - x[1] - 2 * x[2] + 3.0)) *

cos(-sqrt(5) * pi * t + pi * x[1] + 2 * pi * x[2] + 1)^3 -

8.0e-9 * sqrt(5) * sin(-sqrt(5) * pi * t + pi * x[1] + 2 * pi * x[2] + 1) *

cos(pi * (sqrt(5) * t - x[1] - 2 * x[2] + 3.0))^2 *

cos(-sqrt(5) * pi * t + pi * x[1] + 2 * pi * x[2] + 1)^2 -

2.0e-5 * sqrt(5) * sin(-sqrt(5) * pi * t + pi * x[1] + 2 * pi * x[2] + 1) *

cos(pi * (sqrt(5) * t - x[1] - 2 * x[2] + 3.0))^2) /

(-0.04 * sin(pi * x[2]) * sin(-sqrt(5) * pi * t + pi * x[1] + pi * x[2] + 1) +

0.02 * cos(-sqrt(5) * pi * t + pi * x[1] + 1) - 1.0)^4

r_6 = pi * (-0.04 *

(sqrt(5) * pi * eta_const * cos(pi * (-sqrt(5) * t + x[1] + 2 * x[2])) +

sin(pi * (-sqrt(5) * t + x[1] + 2 * x[2]))) *

(0.02 * cos(-sqrt(5) * pi * t + pi * (x[1] + 2 * x[2] - 3.0) + 1) + 1)^2 +

0.04 * (0.02 * cos(-sqrt(5) * pi * t + pi * (x[1] + 2 * x[2] - 3.0) + 1) + 1) *

sin(pi * (-sqrt(5) * t + x[1] + 2 * x[2])) +

0.0004 * sin(-2 * sqrt(5) * pi * t + 2 * pi * x[1] + 4 * pi * x[2] + 1) +

0.0004 * sin(1)) /

(0.02 * cos(-sqrt(5) * pi * t + pi * (x[1] + 2 * x[2] - 3.0) + 1) + 1)^2

r_7 = pi * (0.02 *

(sqrt(5) * pi * eta_const * cos(pi * (-sqrt(5) * t + x[1] + 2 * x[2])) +

sin(pi * (-sqrt(5) * t + x[1] + 2 * x[2]))) *

(0.02 * cos(-sqrt(5) * pi * t + pi * (x[1] + 2 * x[2] - 3.0) + 1) + 1)^2 -

0.02 * (0.02 * cos(-sqrt(5) * pi * t + pi * (x[1] + 2 * x[2] - 3.0) + 1) + 1) *

sin(pi * (-sqrt(5) * t + x[1] + 2 * x[2])) -

0.0002 * sin(-2 * sqrt(5) * pi * t + 2 * pi * x[1] + 4 * pi * x[2] + 1) -

0.0002 * sin(1)) /

(0.02 * cos(-sqrt(5) * pi * t + pi * (x[1] + 2 * x[2] - 3.0) + 1) + 1)^2

r_8 = pi * ((0.1 * pi * eta_const * sin(pi * (-sqrt(5) * t + x[1] + 2 * x[2])) +

0.02 * sqrt(5) * cos(pi * (sqrt(5) * t - x[1] - 2 * x[2] + 3.0))) *

(0.02 * cos(-sqrt(5) * pi * t + pi * (x[1] + 2 * x[2] - 3.0) + 1) + 1)^2 -

0.02 * sqrt(5) *

(0.02 * cos(-sqrt(5) * pi * t + pi * (x[1] + 2 * x[2] - 3.0) + 1) + 1) *

cos(pi * (sqrt(5) * t - x[1] - 2 * x[2] + 3.0)) +

0.0002 * sqrt(5) *

(cos(-2 * sqrt(5) * pi * t + 2 * pi * x[1] + 4 * pi * x[2] + 1) - cos(1))) /

(0.02 * cos(-sqrt(5) * pi * t + pi * (x[1] + 2 * x[2] - 3.0) + 1) + 1)^2

github-actions · 2026-04-29T17:08:40Z

[JuliaFormatter] _{reported by reviewdog 🐶}

Trixi.jl/src/semidiscretization/semidiscretization_hyperbolic_parabolic.jl

Lines 14 to 21 in 9c1675c

mutable struct SemidiscretizationHyperbolicParabolic{Mesh, Equations, EquationsParabolic,

InitialCondition,

BoundaryConditions,

BoundaryConditionsParabolic,

SourceTerms, SourceTermsParabolic,

Solver, SolverParabolic,

Cache, CacheParabolic} <:

AbstractSemidiscretization

github-actions · 2026-04-30T10:11:52Z

 include("compressible_navier_stokes.jl")
+
+include("visco_resistive_mhd_3d.jl")
+


[JuliaFormatter] _{reported by reviewdog 🐶}

Suggested change

github-actions · 2026-04-30T10:26:34Z

+    ViscoResistiveMhd3D{typeof(gradient_variables), typeof(gamma), typeof(equations)
+                        }(gamma, inv_gamma_minus_one,
+                          μ, Pr, eta, kappa,
+                          equations, gradient_variables)


[JuliaFormatter] _{reported by reviewdog 🐶}

Suggested change

ViscoResistiveMhd3D{typeof(gradient_variables), typeof(gamma), typeof(equations)

}(gamma, inv_gamma_minus_one,

μ, Pr, eta, kappa,

equations, gradient_variables)

ViscoResistiveMhd3D{typeof(gradient_variables), typeof(gamma), typeof(equations)}(gamma,

inv_gamma_minus_one,

μ,

Pr,

eta,

kappa,

equations,

gradient_variables)

github-actions · 2026-04-30T10:26:34Z

+                                                  equations::ViscoResistiveMhd3D{
+                                                                                 GradientVariablesPrimitive
+                                                                                 })


[JuliaFormatter] _{reported by reviewdog 🐶}

Suggested change

equations::ViscoResistiveMhd3D{

GradientVariablesPrimitive

})

equations::ViscoResistiveMhd3D{GradientVariablesPrimitive})

github-actions · 2026-04-30T10:26:34Z

+                                                 ::ViscoResistiveMhd3D{
+                                                                       GradientVariablesPrimitive
+                                                                       })


[JuliaFormatter] _{reported by reviewdog 🐶}

Suggested change

::ViscoResistiveMhd3D{

GradientVariablesPrimitive

})

::ViscoResistiveMhd3D{GradientVariablesPrimitive})

andrewwinters5000 and others added 30 commits October 18, 2022 19:25

initial commit of 3d approximation for CNS

d5cf820

typo fix in CNS 2D file

b5e1354

add TGV elixir for compressible Navier-Stokes

ab9329c

add DGMulti CNS 3D elixir

82369ec

need TreeMesh versions of slip wall BC in 3D compressible Euler for c…

5929572

…onvergence testing

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9267369

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01b3752

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2921f1d

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bfb7114

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110b5fa

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bfccb07

add battery of 3D parabolic tests. All pass locally

323e4cf

remove old comments and TODOs

1929552

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559f47c

Merge branch 'main' into ns-treemesh-3d

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Merge branch 'ns-treemesh-3d' of github.com:trixi-framework/Trixi.jl …

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Merge branch 'main' into ns-treemesh-3d

6fdec4b

add vorticity and enstrophy functions

2f05140

add first version of an enstrophy callback

54ff12a

add enstrophy callback to TGV elixir

91bb5a1

Merge branch 'ns-treemesh-3d' of github.com:trixi-framework/Trixi.jl …

fc46ae1

…into ns-treemesh-3d

update TGV test values since switched surface flux to flux_hllc

104b8c8

Merge branch 'main' into ns-treemesh-3d

aa7da6f

adding draft DGMulti analysis callback

8416705

adding draft DGMulti analysis callback

28c3eca

forgot the return statement

Merge remote-tracking branch 'refs/remotes/origin/ns-treemesh-3d'

383ccfe

Conflicts: src/callbacks_step/analysis_dgmulti.jl

Merge branch 'main' into ns-treemesh-3d

315f448

Apply suggestions from code review

5f9e40b

Co-authored-by: Hendrik Ranocha <ranocha@users.noreply.github.com>

make sure Experimental code text renders properly in docs

c512038

adding extra analysis integrals

8c2e242

SimonCan and others added 3 commits February 16, 2024 18:18

Corrected residual for 3d Alfven wave for the visco-resistive MHD con…

3421b6e

…vergence test.

Apple autoformatter on the lengthy expressions for the residuals.

8100a68

Merge branch 'main' into sc/mhd-treemesh-3d

e7d95a1

SimonCan and others added 4 commits February 22, 2024 10:56

Simplifie terms for visco-resistive MHD convergence.

e682381

Removed small numbers that should be 0. Does not affect convergence n…

7497cda

…umbers.

Merge branch 'main' into sc/mhd-treemesh-3d

279d0cf

Further convergence tests.

a941f28

DanielDoehring changed the title ~~Sc/mhd treemesh 3d~~ Sc/VR-MHD treemesh 3d Jun 29, 2025

Merge branch 'main' into sc/mhd-treemesh-3d

e5712b8

DanielDoehring mentioned this pull request Mar 21, 2026

Convergence Test MHD 3D (Non-Alfwen Wave) #2875

Merged

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SimonCan changed the title ~~Sc/VR-MHD treemesh 3d~~ Sc/MHD treemesh 3d Apr 29, 2026

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SimonCan changed the title ~~WIP: Sc/mhd treemesh 2d~~ WIP: Sc/mhd treemesh 3d Apr 29, 2026

SimonCan added 3 commits April 29, 2026 14:17

Add explicit (boundary_condition_periodic, boundary_condition_periodi…

b867d90

…c) pass. Add periodicity = True, as it is not default anymore. Make SemidiscretizationHyperbolicParabolic mutable.

git pushMerge branch 'sc/mhd-treemesh-3d' of github.com:trixi-framewo…

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…rk/Trixi.jl into sc/mhd-treemesh-3d

Fixed parameters for speedy convergence tests.

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-    r_1 = 0.02*sqrt(5)*pi*sin(-sqrt(5)*pi*t + pi*(x[1] + 2*x[2] - 3.0) + 1)
-    r_2 = sqrt(5)*pi^2*mu_const*(-0.04*(0.02*cos(-sqrt(5)*pi*t + pi*(x[1] + 2*x[2] - 3.0) + 1) + 1)^2*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0)) + (0.02*cos(-sqrt(5)*pi*t + pi*(x[1] + 2*x[2] - 3.0) + 1) + 1)*(0.0012*cos(-2*sqrt(5)*pi*t + 2*pi*x[1] + 4*pi*x[2] + 1) - 0.0004*cos(1)) + 3.2e-5*sin(-sqrt(5)*pi*t + pi*(x[1] + 2*x[2] - 3.0) + 1)^2*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0)))/(0.02*cos(-sqrt(5)*pi*t + pi*(x[1] + 2*x[2] - 3.0) + 1) + 1)^3
-    r_3 = -sqrt(5)*pi^2*mu_const*(-0.02*(0.02*cos(-sqrt(5)*pi*t + pi*(x[1] + 2*x[2] - 3.0) + 1) + 1)^2*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0)) + (0.02*cos(-sqrt(5)*pi*t + pi*(x[1] + 2*x[2] - 3.0) + 1) + 1)*(0.0006*cos(-2*sqrt(5)*pi*t + 2*pi*x[1] + 4*pi*x[2] + 1) - 0.0002*cos(1)) + 1.6e-5*sin(-sqrt(5)*pi*t + pi*(x[1] + 2*x[2] - 3.0) + 1)^2*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0)))/(0.02*cos(-sqrt(5)*pi*t + pi*(x[1] + 2*x[2] - 3.0) + 1) + 1)^3
-    r_4 = -pi^2*mu_const*((0.003*sin(-2*sqrt(5)*pi*t + 2*pi*x[1] + 4*pi*x[2] + 1) + 0.001*sin(1))*(0.02*cos(-sqrt(5)*pi*t + pi*(x[1] + 2*x[2] - 3.0) + 1) + 1) + 0.1*(0.02*cos(-sqrt(5)*pi*t + pi*(x[1] + 2*x[2] - 3.0) + 1) + 1)^2*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2])) - 8.0e-5*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))*sin(-sqrt(5)*pi*t + pi*(x[1] + 2*x[2] - 3.0) + 1)^2)/(0.02*cos(-sqrt(5)*pi*t + pi*(x[1] + 2*x[2] - 3.0) + 1) + 1)^3
-#     r_5 = 0.2*pi*(2.77777777777778e-7*pi*mu_const*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))^2*sin(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1) -2.58888888888889e-5*pi*mu_const*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))^2*sin(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^2 + 1.38888888888889e-7*pi*mu_const*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^3 - 1.78888888888889e-5*pi*mu_const*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^2 + 0.000547222222222222*pi*mu_const*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1) + 2.77777777777778e-7*pi*mu_const*sin(-sqrt(5)*pi*t +pi*x[1] + 2*pi*x[2] + 1)^2*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1) - 2.58888888888889e-5*pi*mu_const*sin(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^2*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0))^2 + 1.38888888888889e-7*pi*mu_const*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^3 - 1.78888888888889e-5*pi*mu_const*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^2 + 0.000547222222222223*pi*mu_const*cos(pi*(sqrt(5)*t - x[1] -2*x[2] + 3.0))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1) + 1.0e-7*sqrt(5)*(-sin(-4*sqrt(5)*pi*t + 4*pi*x[1] + 8*pi*x[2] + 2) + 2*sin(-2*sqrt(5)*pi*t + 2*pi*x[1] + 4*pi*x[2] + 2) - sin(2)) + 1.0e-7*sqrt(5)*(sin(-4*sqrt(5)*pi*t + 4*pi*x[1] + 8*pi*x[2] + 2) + 2*sin(-2*sqrt(5)*pi*t + 2*pi*x[1] + 4*pi*x[2] + 2) + sin(2)) - 8.0e-9*sqrt(5)*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))^2*sin(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^2 - 2.0e-5*sqrt(5)*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))^2*sin(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1) - 8.0e-9*sqrt(5)*sin(-sqrt(5)*pi*t+ pi*x[1] + 2*pi*x[2] + 1)*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^2 - 2.0e-5*sqrt(5)*sin(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0))^2)/(-0.04*sin(pi*x[2])*sin(-sqrt(5)*pi*t + pi*x[1] + pi*x[2] + 1) + 0.02*cos(-sqrt(5)*pi*t + pi*x[1] + 1) - 1.0)^4
-    r_5 = 0.2*pi*(1.7205356741103e-21*pi*mu_const*(cos(-4*sqrt(5)*pi*t + 4*pi*x[1] + 8*pi*x[2] + 2) - cos(2)) - 1.01643953670516e-19*pi*mu_const*(cos(-3*sqrt(5)*pi*t + 3*pi*x[1] + 6*pi*x[2] + 1) - cos(sqrt(5)*pi*t - pi*x[1] - 2*pi*x[2] + 1)) + 2.77777777777778e-7*pi*mu_const*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))^2*sin(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1) - 2.58888888888889e-5*pi*mu_const*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))^2*sin(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^2 + 1.38888888888889e-7*pi*mu_const*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^3 - 1.78888888888889e-5*pi*mu_const*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^2 + 0.000547222222222222*pi*mu_const*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1) + 4.33680868994202e-18*pi*mu_const*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))^2 - 1.17643464896431e-22*pi*mu_const*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))*sin(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0))*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^2 + 2.77777777777778e-7*pi*mu_const*sin(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^2*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1) - 2.58888888888889e-5*pi*mu_const*sin(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^2*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0))^2 - 2.16840434497101e-25*pi*mu_const*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^4 + 1.38888888888889e-7*pi*mu_const*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^3 - 1.78888888888889e-5*pi*mu_const*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^2 + 0.000547222222222223*pi*mu_const*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1) - 6.64073830647371e-18*pi*mu_const*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0))^2 + 1.0842021724855e-21*sqrt(5)*(-sin(-3*sqrt(5)*pi*t + 3*pi*x[1] + 6*pi*x[2] + 1) + sin(sqrt(5)*pi*t - pi*x[1] - 2*pi*x[2] + 1)) + 1.0842021724855e-27*sqrt(5)*(cos(-2*sqrt(5)*pi*t + 2*pi*x[1] + 4*pi*x[2] + 2) + 1)^2*sin(pi*(-2*sqrt(5)*t + 2*x[1] + 4*x[2])) - 1.62630325872826e-23*sqrt(5)*(-2*sin(pi*(-2*sqrt(5)*t + 2*x[1] + 4*x[2])) - sin(-4*sqrt(5)*pi*t + 4*pi*x[1] + 8*pi*x[2] + 2) + sin(2)) + 1.0e-7*sqrt(5)*(-sin(-4*sqrt(5)*pi*t + 4*pi*x[1] + 8*pi*x[2] + 2) + 2*sin(-2*sqrt(5)*pi*t + 2*pi*x[1] + 4*pi*x[2] + 2) - sin(2)) + 1.0e-7*sqrt(5)*(sin(-4*sqrt(5)*pi*t + 4*pi*x[1] + 8*pi*x[2] + 2) + 2*sin(-2*sqrt(5)*pi*t + 2*pi*x[1] + 4*pi*x[2] + 2) + sin(2)) + 2.71050543121376e-20*sqrt(5)*sin(pi*(-2*sqrt(5)*t + 2*x[1] + 4*x[2])) - 8.0e-9*sqrt(5)*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))^2*sin(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^2 - 2.0e-5*sqrt(5)*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))^2*sin(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1) + 1.73472347597681e-24*sqrt(5)*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0))*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^3 - 8.0e-9*sqrt(5)*sin(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^2 - 2.0e-5*sqrt(5)*sin(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0))^2)/(-0.04*sin(pi*x[2])*sin(-sqrt(5)*pi*t + pi*x[1] + pi*x[2] + 1) + 0.02*cos(-sqrt(5)*pi*t + pi*x[1] + 1) - 1.0)^4
-    r_6 = pi*(-0.04*(sqrt(5)*pi*eta_const*cos(pi*(-sqrt(5)*t + x[1] + 2*x[2])) + sin(pi*(-sqrt(5)*t + x[1] + 2*x[2])))*(0.02*cos(-sqrt(5)*pi*t + pi*(x[1] + 2*x[2] - 3.0) + 1) + 1)^2 + 0.04*(0.02*cos(-sqrt(5)*pi*t + pi*(x[1] + 2*x[2] - 3.0) + 1) + 1)*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2])) + 0.0004*sin(-2*sqrt(5)*pi*t + 2*pi*x[1] + 4*pi*x[2] + 1) + 0.0004*sin(1))/(0.02*cos(-sqrt(5)*pi*t + pi*(x[1] + 2*x[2] - 3.0) + 1) + 1)^2
-    r_7 = pi*(0.02*(sqrt(5)*pi*eta_const*cos(pi*(-sqrt(5)*t + x[1] + 2*x[2])) + sin(pi*(-sqrt(5)*t + x[1] + 2*x[2])))*(0.02*cos(-sqrt(5)*pi*t + pi*(x[1] + 2*x[2] - 3.0) + 1) + 1)^2 - 0.02*(0.02*cos(-sqrt(5)*pi*t + pi*(x[1] + 2*x[2] - 3.0) + 1) + 1)*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2])) - 0.0002*sin(-2*sqrt(5)*pi*t + 2*pi*x[1] + 4*pi*x[2] + 1) - 0.0002*sin(1))/(0.02*cos(-sqrt(5)*pi*t + pi*(x[1]+ 2*x[2] - 3.0) + 1) + 1)^2
-    r_8 = pi*((0.1*pi*eta_const*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2])) + 0.02*sqrt(5)*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0)))*(0.02*cos(-sqrt(5)*pi*t + pi*(x[1] + 2*x[2] - 3.0) + 1) + 1)^2 - 0.02*sqrt(5)*(0.02*cos(-sqrt(5)*pi*t + pi*(x[1] + 2*x[2] - 3.0) + 1) +1)*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0)) + 0.0002*sqrt(5)*(cos(-2*sqrt(5)*pi*t + 2*pi*x[1] + 4*pi*x[2] + 1) - cos(1)))/(0.02*cos(-sqrt(5)*pi*t + pi*(x[1] + 2*x[2] - 3.0) + 1) + 1)^2
+    r_1 = 0.02 * sqrt(5) * pi * sin(-sqrt(5) * pi * t + pi * (x[1] + 2 * x[2] - 3.0) + 1)
+    r_2 = sqrt(5) * pi^2 * mu_const *
+          (-0.04 *
+           (0.02 * cos(-sqrt(5) * pi * t + pi * (x[1] + 2 * x[2] - 3.0) + 1) + 1)^2 *
+           cos(pi * (sqrt(5) * t - x[1] - 2 * x[2] + 3.0)) +
+           (0.02 * cos(-sqrt(5) * pi * t + pi * (x[1] + 2 * x[2] - 3.0) + 1) + 1) *
+           (0.0012 * cos(-2 * sqrt(5) * pi * t + 2 * pi * x[1] + 4 * pi * x[2] + 1) -
+.0004 * cos(1)) +
+.2e-5 * sin(-sqrt(5) * pi * t + pi * (x[1] + 2 * x[2] - 3.0) + 1)^2 *
+           cos(pi * (sqrt(5) * t - x[1] - 2 * x[2] + 3.0))) /
+          (0.02 * cos(-sqrt(5) * pi * t + pi * (x[1] + 2 * x[2] - 3.0) + 1) + 1)^3
+    r_3 = -sqrt(5) * pi^2 * mu_const *
+          (-0.02 *
+           (0.02 * cos(-sqrt(5) * pi * t + pi * (x[1] + 2 * x[2] - 3.0) + 1) + 1)^2 *
+           cos(pi * (sqrt(5) * t - x[1] - 2 * x[2] + 3.0)) +
+           (0.02 * cos(-sqrt(5) * pi * t + pi * (x[1] + 2 * x[2] - 3.0) + 1) + 1) *
+           (0.0006 * cos(-2 * sqrt(5) * pi * t + 2 * pi * x[1] + 4 * pi * x[2] + 1) -
+.0002 * cos(1)) +
+.6e-5 * sin(-sqrt(5) * pi * t + pi * (x[1] + 2 * x[2] - 3.0) + 1)^2 *
+           cos(pi * (sqrt(5) * t - x[1] - 2 * x[2] + 3.0))) /
+          (0.02 * cos(-sqrt(5) * pi * t + pi * (x[1] + 2 * x[2] - 3.0) + 1) + 1)^3
+    r_4 = -pi^2 * mu_const *
+          ((0.003 * sin(-2 * sqrt(5) * pi * t + 2 * pi * x[1] + 4 * pi * x[2] + 1) +
+.001 * sin(1)) *
+           (0.02 * cos(-sqrt(5) * pi * t + pi * (x[1] + 2 * x[2] - 3.0) + 1) + 1) +
+.1 * (0.02 * cos(-sqrt(5) * pi * t + pi * (x[1] + 2 * x[2] - 3.0) + 1) + 1)^2 *
+           sin(pi * (-sqrt(5) * t + x[1] + 2 * x[2])) -
+.0e-5 * sin(pi * (-sqrt(5) * t + x[1] + 2 * x[2])) *
+           sin(-sqrt(5) * pi * t + pi * (x[1] + 2 * x[2] - 3.0) + 1)^2) /
+          (0.02 * cos(-sqrt(5) * pi * t + pi * (x[1] + 2 * x[2] - 3.0) + 1) + 1)^3
+    #     r_5 = 0.2*pi*(2.77777777777778e-7*pi*mu_const*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))^2*sin(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1) -2.58888888888889e-5*pi*mu_const*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))^2*sin(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^2 + 1.38888888888889e-7*pi*mu_const*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^3 - 1.78888888888889e-5*pi*mu_const*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^2 + 0.000547222222222222*pi*mu_const*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1) + 2.77777777777778e-7*pi*mu_const*sin(-sqrt(5)*pi*t +pi*x[1] + 2*pi*x[2] + 1)^2*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1) - 2.58888888888889e-5*pi*mu_const*sin(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^2*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0))^2 + 1.38888888888889e-7*pi*mu_const*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^3 - 1.78888888888889e-5*pi*mu_const*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^2 + 0.000547222222222223*pi*mu_const*cos(pi*(sqrt(5)*t - x[1] -2*x[2] + 3.0))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1) + 1.0e-7*sqrt(5)*(-sin(-4*sqrt(5)*pi*t + 4*pi*x[1] + 8*pi*x[2] + 2) + 2*sin(-2*sqrt(5)*pi*t + 2*pi*x[1] + 4*pi*x[2] + 2) - sin(2)) + 1.0e-7*sqrt(5)*(sin(-4*sqrt(5)*pi*t + 4*pi*x[1] + 8*pi*x[2] + 2) + 2*sin(-2*sqrt(5)*pi*t + 2*pi*x[1] + 4*pi*x[2] + 2) + sin(2)) - 8.0e-9*sqrt(5)*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))^2*sin(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^2 - 2.0e-5*sqrt(5)*sin(pi*(-sqrt(5)*t + x[1] + 2*x[2]))^2*sin(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1) - 8.0e-9*sqrt(5)*sin(-sqrt(5)*pi*t+ pi*x[1] + 2*pi*x[2] + 1)*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0))^2*cos(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)^2 - 2.0e-5*sqrt(5)*sin(-sqrt(5)*pi*t + pi*x[1] + 2*pi*x[2] + 1)*cos(pi*(sqrt(5)*t - x[1] - 2*x[2] + 3.0))^2)/(-0.04*sin(pi*x[2])*sin(-sqrt(5)*pi*t + pi*x[1] + pi*x[2] + 1) + 0.02*cos(-sqrt(5)*pi*t + pi*x[1] + 1) - 1.0)^4
+    r_5 = 0.2 * pi *
+          (1.7205356741103e-21 * pi * mu_const *
+           (cos(-4 * sqrt(5) * pi * t + 4 * pi * x[1] + 8 * pi * x[2] + 2) - cos(2)) -
+.01643953670516e-19 * pi * mu_const *
+           (cos(-3 * sqrt(5) * pi * t + 3 * pi * x[1] + 6 * pi * x[2] + 1) -
+            cos(sqrt(5) * pi * t - pi * x[1] - 2 * pi * x[2] + 1)) +
+.77777777777778e-7 * pi * mu_const *
+           sin(pi * (-sqrt(5) * t + x[1] + 2 * x[2]))^2 *
+           sin(-sqrt(5) * pi * t + pi * x[1] + 2 * pi * x[2] + 1)^2 *
+           cos(-sqrt(5) * pi * t + pi * x[1] + 2 * pi * x[2] + 1) -
+.58888888888889e-5 * pi * mu_const *
+           sin(pi * (-sqrt(5) * t + x[1] + 2 * x[2]))^2 *
+           sin(-sqrt(5) * pi * t + pi * x[1] + 2 * pi * x[2] + 1)^2 +
+.38888888888889e-7 * pi * mu_const *
+           sin(pi * (-sqrt(5) * t + x[1] + 2 * x[2]))^2 *
+           cos(-sqrt(5) * pi * t + pi * x[1] + 2 * pi * x[2] + 1)^3 -
+.78888888888889e-5 * pi * mu_const *
+           sin(pi * (-sqrt(5) * t + x[1] + 2 * x[2]))^2 *
+           cos(-sqrt(5) * pi * t + pi * x[1] + 2 * pi * x[2] + 1)^2 +
+.000547222222222222 * pi * mu_const *
+           sin(pi * (-sqrt(5) * t + x[1] + 2 * x[2]))^2 *
+           cos(-sqrt(5) * pi * t + pi * x[1] + 2 * pi * x[2] + 1) +
+.33680868994202e-18 * pi * mu_const *
+           sin(pi * (-sqrt(5) * t + x[1] + 2 * x[2]))^2 -
+.17643464896431e-22 * pi * mu_const *
+           sin(pi * (-sqrt(5) * t + x[1] + 2 * x[2])) *
+           sin(-sqrt(5) * pi * t + pi * x[1] + 2 * pi * x[2] + 1) *
+           cos(pi * (sqrt(5) * t - x[1] - 2 * x[2] + 3.0)) *
+           cos(-sqrt(5) * pi * t + pi * x[1] + 2 * pi * x[2] + 1)^2 +
+.77777777777778e-7 * pi * mu_const *
+           sin(-sqrt(5) * pi * t + pi * x[1] + 2 * pi * x[2] + 1)^2 *
+           cos(pi * (sqrt(5) * t - x[1] - 2 * x[2] + 3.0))^2 *
+           cos(-sqrt(5) * pi * t + pi * x[1] + 2 * pi * x[2] + 1) -
+.58888888888889e-5 * pi * mu_const *
+           sin(-sqrt(5) * pi * t + pi * x[1] + 2 * pi * x[2] + 1)^2 *
+           cos(pi * (sqrt(5) * t - x[1] - 2 * x[2] + 3.0))^2 -
+.16840434497101e-25 * pi * mu_const *
+           cos(pi * (sqrt(5) * t - x[1] - 2 * x[2] + 3.0))^2 *
+           cos(-sqrt(5) * pi * t + pi * x[1] + 2 * pi * x[2] + 1)^4 +
+.38888888888889e-7 * pi * mu_const *
+           cos(pi * (sqrt(5) * t - x[1] - 2 * x[2] + 3.0))^2 *
+           cos(-sqrt(5) * pi * t + pi * x[1] + 2 * pi * x[2] + 1)^3 -
+.78888888888889e-5 * pi * mu_const *
+           cos(pi * (sqrt(5) * t - x[1] - 2 * x[2] + 3.0))^2 *
+           cos(-sqrt(5) * pi * t + pi * x[1] + 2 * pi * x[2] + 1)^2 +
+.000547222222222223 * pi * mu_const *
+           cos(pi * (sqrt(5) * t - x[1] - 2 * x[2] + 3.0))^2 *
+           cos(-sqrt(5) * pi * t + pi * x[1] + 2 * pi * x[2] + 1) -
+.64073830647371e-18 * pi * mu_const *
+           cos(pi * (sqrt(5) * t - x[1] - 2 * x[2] + 3.0))^2 +
+.0842021724855e-21 * sqrt(5) *
+           (-sin(-3 * sqrt(5) * pi * t + 3 * pi * x[1] + 6 * pi * x[2] + 1) +
+            sin(sqrt(5) * pi * t - pi * x[1] - 2 * pi * x[2] + 1)) +
+.0842021724855e-27 * sqrt(5) *
+           (cos(-2 * sqrt(5) * pi * t + 2 * pi * x[1] + 4 * pi * x[2] + 2) + 1)^2 *
+           sin(pi * (-2 * sqrt(5) * t + 2 * x[1] + 4 * x[2])) -
+.62630325872826e-23 * sqrt(5) *
+           (-2 * sin(pi * (-2 * sqrt(5) * t + 2 * x[1] + 4 * x[2])) -
+            sin(-4 * sqrt(5) * pi * t + 4 * pi * x[1] + 8 * pi * x[2] + 2) + sin(2)) +
+.0e-7 * sqrt(5) *
+           (-sin(-4 * sqrt(5) * pi * t + 4 * pi * x[1] + 8 * pi * x[2] + 2) +
+* sin(-2 * sqrt(5) * pi * t + 2 * pi * x[1] + 4 * pi * x[2] + 2) - sin(2)) +
+.0e-7 * sqrt(5) *
+           (sin(-4 * sqrt(5) * pi * t + 4 * pi * x[1] + 8 * pi * x[2] + 2) +
+* sin(-2 * sqrt(5) * pi * t + 2 * pi * x[1] + 4 * pi * x[2] + 2) + sin(2)) +
+.71050543121376e-20 * sqrt(5) *
+           sin(pi * (-2 * sqrt(5) * t + 2 * x[1] + 4 * x[2])) -
+.0e-9 * sqrt(5) * sin(pi * (-sqrt(5) * t + x[1] + 2 * x[2]))^2 *
+           sin(-sqrt(5) * pi * t + pi * x[1] + 2 * pi * x[2] + 1) *
+           cos(-sqrt(5) * pi * t + pi * x[1] + 2 * pi * x[2] + 1)^2 -
+.0e-5 * sqrt(5) * sin(pi * (-sqrt(5) * t + x[1] + 2 * x[2]))^2 *
+           sin(-sqrt(5) * pi * t + pi * x[1] + 2 * pi * x[2] + 1) +
+.73472347597681e-24 * sqrt(5) * sin(pi * (-sqrt(5) * t + x[1] + 2 * x[2])) *
+           cos(pi * (sqrt(5) * t - x[1] - 2 * x[2] + 3.0)) *
+           cos(-sqrt(5) * pi * t + pi * x[1] + 2 * pi * x[2] + 1)^3 -
+.0e-9 * sqrt(5) * sin(-sqrt(5) * pi * t + pi * x[1] + 2 * pi * x[2] + 1) *
+           cos(pi * (sqrt(5) * t - x[1] - 2 * x[2] + 3.0))^2 *
+           cos(-sqrt(5) * pi * t + pi * x[1] + 2 * pi * x[2] + 1)^2 -
+.0e-5 * sqrt(5) * sin(-sqrt(5) * pi * t + pi * x[1] + 2 * pi * x[2] + 1) *
+           cos(pi * (sqrt(5) * t - x[1] - 2 * x[2] + 3.0))^2) /
+          (-0.04 * sin(pi * x[2]) * sin(-sqrt(5) * pi * t + pi * x[1] + pi * x[2] + 1) +
+.02 * cos(-sqrt(5) * pi * t + pi * x[1] + 1) - 1.0)^4
+    r_6 = pi * (-0.04 *
+           (sqrt(5) * pi * eta_const * cos(pi * (-sqrt(5) * t + x[1] + 2 * x[2])) +
+            sin(pi * (-sqrt(5) * t + x[1] + 2 * x[2]))) *
+           (0.02 * cos(-sqrt(5) * pi * t + pi * (x[1] + 2 * x[2] - 3.0) + 1) + 1)^2 +
+.04 * (0.02 * cos(-sqrt(5) * pi * t + pi * (x[1] + 2 * x[2] - 3.0) + 1) + 1) *
+           sin(pi * (-sqrt(5) * t + x[1] + 2 * x[2])) +
+.0004 * sin(-2 * sqrt(5) * pi * t + 2 * pi * x[1] + 4 * pi * x[2] + 1) +
+.0004 * sin(1)) /
+          (0.02 * cos(-sqrt(5) * pi * t + pi * (x[1] + 2 * x[2] - 3.0) + 1) + 1)^2
+    r_7 = pi * (0.02 *
+           (sqrt(5) * pi * eta_const * cos(pi * (-sqrt(5) * t + x[1] + 2 * x[2])) +
+            sin(pi * (-sqrt(5) * t + x[1] + 2 * x[2]))) *
+           (0.02 * cos(-sqrt(5) * pi * t + pi * (x[1] + 2 * x[2] - 3.0) + 1) + 1)^2 -
+.02 * (0.02 * cos(-sqrt(5) * pi * t + pi * (x[1] + 2 * x[2] - 3.0) + 1) + 1) *
+           sin(pi * (-sqrt(5) * t + x[1] + 2 * x[2])) -
+.0002 * sin(-2 * sqrt(5) * pi * t + 2 * pi * x[1] + 4 * pi * x[2] + 1) -
+.0002 * sin(1)) /
+          (0.02 * cos(-sqrt(5) * pi * t + pi * (x[1] + 2 * x[2] - 3.0) + 1) + 1)^2
+    r_8 = pi * ((0.1 * pi * eta_const * sin(pi * (-sqrt(5) * t + x[1] + 2 * x[2])) +
+.02 * sqrt(5) * cos(pi * (sqrt(5) * t - x[1] - 2 * x[2] + 3.0))) *
+           (0.02 * cos(-sqrt(5) * pi * t + pi * (x[1] + 2 * x[2] - 3.0) + 1) + 1)^2 -
+.02 * sqrt(5) *
+           (0.02 * cos(-sqrt(5) * pi * t + pi * (x[1] + 2 * x[2] - 3.0) + 1) + 1) *
+           cos(pi * (sqrt(5) * t - x[1] - 2 * x[2] + 3.0)) +
+.0002 * sqrt(5) *
+           (cos(-2 * sqrt(5) * pi * t + 2 * pi * x[1] + 4 * pi * x[2] + 1) - cos(1))) /
+          (0.02 * cos(-sqrt(5) * pi * t + pi * (x[1] + 2 * x[2] - 3.0) + 1) + 1)^2

	mutable struct SemidiscretizationHyperbolicParabolic{Mesh, Equations, EquationsParabolic,
	InitialCondition,
	BoundaryConditions,
	BoundaryConditionsParabolic,
	SourceTerms, SourceTermsParabolic,
	Solver, SolverParabolic,
	Cache, CacheParabolic} <:
	AbstractSemidiscretization

		include("compressible_navier_stokes.jl")

		include("visco_resistive_mhd_3d.jl")

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SimonCan commented Jan 10, 2023 •

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