Examples with manufactured solutions

In this section we describe numerous examples that mainly involve manufactured solutions on hydrodynamic, magnetic and MHD set ups. These tests have been implemented in the code SFEMaNS so users can check that the installation of SFEMaNS and the required softwares (PETSC, ARPACK, etc.) have been done correctly. These tests can be run with the shell debug_SFEMaNS_template. We refer to the section Check Installation for more information on how to check the correct installation of the code SFEMaNS.

We note that these tests don't read the information in condlim.f90, read_user_data.f90 and main.f90:

1. The initial/boundary conditions and forcing term are read in a condlim file specific for each test. They can be found in the following directory: ($SFEMaNS_DIR)/MHD_DATA_TEST_CONV_PETSC/. They are named condlim_test_nb_test with nb_test the number of the test.
2. Each test uses its own data that are in the following directory: ($SFEMaNS_DIR)/MHD_DATA_TEST_CONV_PETSC/. They are named debug_data_nb_test with nb_test the number of the test.
3. As these tests compute similar outputs, the postprocessing is done via the same fortran file post_processing_debug.f90. It can be found in the following directory: ($SFEMaNS_DIR)/MHD_DATA_TEST_CONV_PETSC.

The description of each of these tests follows this structure:

1. Introduction: describe the purpose of the test and the equations to solve.
2. Manufactured solutions: introduce the solutions considered.
3. Generation of the mesh: information on the mesh and its topology.
4. Information on the file condlim: describe the implementation of initial/boundary conditions and source terms.
5. Setting in the data file: description of the data file.
6. Outputs and value of reference: describe outputs considered and the values to recover with SFEMaNS.

Here is the list of the tests. Their respective title provide information on the equations involved.

Test 1: Navier-Stokes

Test 2: Navier-Stokes periodic

Test 3: Maxwell with vacuum P2-P2

Test 4: Maxwell with vacuum periodic P1-P2

Test 5: Maxwell with vacuum P1-P2

Test 6: Maxwell variable permeability with vacuum P1-P2

Test 7: Maxwell with vacuum P2-P2

Test 8: Navier-Stokes with Temperature

Test 9: Navier-Stokes with Temperature periodic

Test 10: Maxwell P2

Test 11: MHD with Temperature and precession

Test 12: Maxwell P1 Neumann bdy

Test 13: MHD periodic and Neumann bdy

Test 14: ARPACK for Maxwell and eigen values problem

Test 15: Navier-Stokes with Temperature and LES

Test 16: Navier-Stokes Neumann bdy with precession

Test 17: Maxwell Equations with vacuum and variable magnetic permeability in (r,z)

Test 18: Maxwell Equations with variable magnetic permeability in (r,z) with jumps

Test 19: Navier-Stokes with variable density

Test 20: restart of test 19 (Navier-Stokes with variable density)

Test 21: MHD with variable density and electrical conductivity

Test 22: Maxwell Equations with vaccum and variable magnetic permeability in (r,theta,z)

Test 23 Maxwell Equations with variable magnetic permeability in (r, theta, z) with jumps

Test 24: Navier-Stokes with penalty for non axisymetric domain

Test 25: Navier-Stokes with variable density and viscosity

Test 26: Maxwell Equations with variable magnetic permeability in z and smooth jump.

Test 27: Maxwell Equations with vacuum and variable magnetic permeability in (r,theta,z,t)

Test 28 Hydrodynamic Simulation of the VKS Experiment

Test 29 MHD Simulation of the VKS Experiment

Test 30: Navier-Stokes with Temperature, temperature computed in a solid and a fluid region

Test 31: Navier-Stokes with Temperature, temperature computed in a solid and a fluid region, periodic manufactured solution and non null pressure

Test 32: Navier-Stokes with Temperature, temperature computed in a solid and a fluid region, periodic manufactured solution and non null pressure, restart from test 31 with interpolation

Test 33: Ferrohydrodynamic

Test 34: Ferrohydrodynamic periodic