test_r13_convergence module

Module to gather tests for convergence of decoupled stress system.

This file is executed by pytest to have good CI.

class test_r13_convergence.TestR13Convergence

Bases: object

Class to bundle all stress convergence tests.

All tests are compared against reference errors.

working_dir = 'tests/2d_r13'

solver_path = 'fenicsR13'

run_solver(inputfile)

Run the solver as subprocess with the given input file.

Test fails if subprocess return Exception or error.

compare_errors(errorsfile, ref_errorsfile)

Check against reference errors. Compares absolute differences.

Absolute Error allowed: 1E-10 Return exception if diff returns with !=0 A comparison for complete equalness can be obtained with:

subprocess.check_call([
    "diff", "-u", "--strip-trailing-cr", errorsfile, ref_errorsfile
], cwd=self.working_dir)

create_meshes()

Create the test meshes. Executed before any test of the class.

Often not needed if meshes are in Git through LFS for reproducability.

test_r13_1_coeffs_nosources_norot_inflow_p1p1p1p1p1_gls()

Execute full linear R13 system test and check with reference errors.

Parameter Value
\(Kn\)	\(1.0\)
\(\dot{m}\)	\(0\)
\(r\)	\(0\)
\(\theta_w^1\)	\(1.0\)
\(v_t^1\)	\(0\)
\(v_n^1\)	\(0\)
\(p_w^1\)	\(0\)
\(\epsilon_w^1\)	\(10^{-3}\)
\(\theta_w^2\)	\(2.0\)
\(v_t^2\)	\(-1.00 \sin(\phi)\)
\(v_n^2\)	\(+1.00 \cos(\phi)\)
\(p_w^2\)	\(-0.27 \cos(\phi)\)
\(\epsilon_w^2\)	\(10^{3}\)
Elements	\(P_1P_1P_1P_1P_1\)
Stabilization	GLS

test_r13_1_coeffs_nosources_norot_inflow_p1p1p1p1p1_stab()

Execute full linear R13 system test and check with reference errors.

Test case is similar to [TOR2017].

Parameter Value
\(Kn\)	\(1.0\)
\(\dot{m}\)	\(0\)
\(r\)	\(0\)
\(\theta_w^1\)	\(1.0\)
\(v_t^1\)	\(0\)
\(v_n^1\)	\(0\)
\(p_w^1\)	\(0\)
\(\epsilon_w^1\)	\(10^{-3}\)
\(\theta_w^2\)	\(2.0\)
\(v_t^2\)	\(-1.00 \sin(\phi)\)
\(v_n^2\)	\(+1.00 \cos(\phi)\)
\(p_w^2\)	\(-0.27 \cos(\phi)\)
\(\epsilon_w^2\)	\(10^{3}\)
Elements	\(P_1P_1P_1P_1P_1\)
Stabilization	CIP: \(\delta_\theta,\delta_u=1,\delta_p=0.01\)

test_r13_1_coeffs_nosources_norot_inflow_p1p2p1p1p2_nostab()

Execute full linear R13 system test and check with reference errors. Use Generalized Taylor-Hood elements (P2P1P2P1P1) w.o. stabilization.

Test case is similar to [TOR2017].

TOR2017(1,2,3)

Torrilhon, M. et al. (2017). “Hierarchical Boltzmann simulations and model error estimation”. In: Journal of Computational Physics 342 (2017), pp. 66–84.

Parameter Value
\(Kn\)	\(1.0\)
\(\dot{m}\)	\(0\)
\(r\)	\(0\)
\(\theta_w^1\)	\(1.0\)
\(v_t^1\)	\(0\)
\(v_n^1\)	\(0\)
\(p_w^1\)	\(0\)
\(\epsilon_w^1\)	\(10^{-3}\)
\(\theta_w^2\)	\(2.0\)
\(v_t^2\)	\(-1.00 \sin(\phi)\)
\(v_n^2\)	\(+1.00 \cos(\phi)\)
\(p_w^2\)	\(-0.27 \cos(\phi)\)
\(\epsilon_w^2\)	\(10^{3}\)
Elements	\(P_1P_2P_1P_1P_2\)
Stabilization	Off

test_r13_1_coeffs_nosources_norot_inflow_p2p2p2p2p2_gls()

Execute full linear R13 system test and check with reference errors. Use second order equal elements.

Parameter Value
\(Kn\)	\(1.0\)
\(\dot{m}\)	\(0\)
\(r\)	\(0\)
\(\theta_w^1\)	\(1.0\)
\(v_t^1\)	\(0\)
\(v_n^1\)	\(0\)
\(p_w^1\)	\(0\)
\(\epsilon_w^1\)	\(10^{-3}\)
\(\theta_w^2\)	\(2.0\)
\(v_t^2\)	\(-1.00 \sin(\phi)\)
\(v_n^2\)	\(+1.00 \cos(\phi)\)
\(p_w^2\)	\(-0.27 \cos(\phi)\)
\(\epsilon_w^2\)	\(10^{3}\)
Elements	\(P_2P_2P_2P_2P_2\)
Stabilization	GLS

test_r13_1_coeffs_nosources_norot_inflow_p2p2p2p2p2_stab()

Execute full linear R13 system test and check with reference errors. Use second order equal elements.

Test case is similar to [TOR2017].

Parameter Value
\(Kn\)	\(1.0\)
\(\dot{m}\)	\(0\)
\(r\)	\(0\)
\(\theta_w^1\)	\(1.0\)
\(v_t^1\)	\(0\)
\(v_n^1\)	\(0\)
\(p_w^1\)	\(0\)
\(\epsilon_w^1\)	\(10^{-3}\)
\(\theta_w^2\)	\(2.0\)
\(v_t^2\)	\(-1.00 \sin(\phi)\)
\(v_n^2\)	\(+1.00 \cos(\phi)\)
\(p_w^2\)	\(-0.27 \cos(\phi)\)
\(\epsilon_w^2\)	\(10^{3}\)
Elements	\(P_2P_2P_2P_2P_2\)
Stabilization	CIP

test_r13_1_coeffs_sources_rot_noinflow_p1p1p1p1p1_gls()

Execute full linear R13 system test and check with reference errors.

Parameter Value
\(Kn\)	\(1.0\)
\(\dot{m}\)	\((1-\frac{5R^2}{18{Kn}^2})\cos(\phi)\)
\(r\)	\(0\)
\(\theta_w^1\)	\(1.0\)
\(v_t^1\)	\(10.0\)
\(v_n^1\)	\(0\)
\(p_w^1\)	\(0\)
\(\epsilon_w^1\)	\(0\)
\(\theta_w^2\)	\(0.5\)
\(v_t^2\)	\(0.0\)
\(v_n^2\)	\(0\)
\(p_w^2\)	\(0\)
\(\epsilon_w^2\)	\(0\)
Elements	\(P_1P_1P_1P_1P_1\)
Stabilization	GLS

test_r13_1_coeffs_sources_rot_noinflow_p1p1p1p1p1_stab()

Execute full linear R13 system test and check with reference errors.

Test case is similar to [WES2019].

WES2019(1,2)

A. Westerkamp and M. Torrilhon. “Finite Element Methods for the Linear Regularized 13-Moment Equations Describing Slow Rarefied Gas Flows”. In: Journal of Computational Physics 389 (2019).

Parameter Value
\(Kn\)	\(1.0\)
\(\dot{m}\)	\((1-\frac{5R^2}{18{Kn}^2})\cos(\phi)\)
\(r\)	\(0\)
\(\theta_w^1\)	\(1.0\)
\(v_t^1\)	\(10.0\)
\(v_n^1\)	\(0\)
\(p_w^1\)	\(0\)
\(\epsilon_w^1\)	\(0\)
\(\theta_w^2\)	\(0.5\)
\(v_t^2\)	\(0.0\)
\(v_n^2\)	\(0\)
\(p_w^2\)	\(0\)
\(\epsilon_w^2\)	\(0\)
Elements	\(P_1P_1P_1P_1P_1\)
Stabilization	CIP: \(\delta_\theta,\delta_u=1,\delta_p=0.01\)

test_r13_1_coeffs_sources_rot_noinflow_p2p2p2p2p2_gls()

Execute full linear R13 system test and check with reference errors.

Parameter Value
\(Kn\)	\(1.0\)
\(\dot{m}\)	\((1-\frac{5R^2}{18{Kn}^2})\cos(\phi)\)
\(r\)	\(0\)
\(\theta_w^1\)	\(1.0\)
\(v_t^1\)	\(10.0\)
\(v_n^1\)	\(0\)
\(p_w^1\)	\(0\)
\(\epsilon_w^1\)	\(0\)
\(\theta_w^2\)	\(0.5\)
\(v_t^2\)	\(0.0\)
\(v_n^2\)	\(0\)
\(p_w^2\)	\(0\)
\(\epsilon_w^2\)	\(0\)
Elements	\(P_2P_2P_2P_2P_2\)
Stabilization	CIP: \(\delta_\theta,\delta_u=1,\delta_p=0.01\)

test_r13_1_coeffs_sources_rot_noinflow_p2p2p2p2p2_stab()

Execute full linear R13 system test and check with reference errors.

Test case is similar to [WES2019].

Parameter Value
\(Kn\)	\(1.0\)
\(\dot{m}\)	\((1-\frac{5R^2}{18{Kn}^2})\cos(\phi)\)
\(r\)	\(0\)
\(\theta_w^1\)	\(1.0\)
\(v_t^1\)	\(10.0\)
\(v_n^1\)	\(0\)
\(p_w^1\)	\(0\)
\(\epsilon_w^1\)	\(0\)
\(\theta_w^2\)	\(0.5\)
\(v_t^2\)	\(0.0\)
\(v_n^2\)	\(0\)
\(p_w^2\)	\(0\)
\(\epsilon_w^2\)	\(0\)
Elements	\(P_2P_2P_2P_2P_2\)
Stabilization	CIP: \(\delta_\theta,\delta_u=1,\delta_p=0.01\)

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