Fix L2Roe, LMRoe and the general-gas Roe scheme in 3D

[rois1995]

Proposed Changes

• 3D flux. Three Roe-type schemes computed part of their numerical dissipation with a 2D formula, also in 3D: L2Roe, LMRoe and the explicit general-gas Roe. So a jump of density or of tangential velocity across a face (a contact or a shear layer) got a wrong flux on faces that are not aligned with the x axis. The standard Roe scheme is already correct (since Consistent calculation of dissipation terms for Roe #299), and 2D is not affected. The three schemes now use the same 3D formula as the standard Roe.

  SU2/SU2_CFD/src/numerics/flow/convection/roe.cpp

  Lines 337 to 339 in a6b7496

  	delta_wave[0] = delta_rho - delta_p/RoeSoundSpeed2;
  	delta_wave[1] = (UnitNormal[0]*delta_vel[2]-UnitNormal[2]*delta_vel[0])*zeta;
  	delta_wave[2] = (UnitNormal[1]*delta_vel[0]-UnitNormal[0]*delta_vel[1])*zeta;

  SU2/SU2_CFD/src/numerics/flow/convection/roe.cpp

  Lines 410 to 412 in a6b7496

  	delta_wave[0] = delta_rho - delta_p/RoeSoundSpeed2;
  	delta_wave[1] = (UnitNormal[0]*delta_vel[2]-UnitNormal[2]*delta_vel[0]);
  	delta_wave[2] = (UnitNormal[1]*delta_vel[0]-UnitNormal[0]*delta_vel[1]);

  SU2/SU2_CFD/src/numerics/flow/convection/roe.cpp

  Lines 904 to 906 in a6b7496

  	delta_wave[0] = delta_rho - delta_p/(RoeSoundSpeed*RoeSoundSpeed);
  	delta_wave[1] = UnitNormal[0]*delta_vel[2]-UnitNormal[2]*delta_vel[0];
  	delta_wave[2] = UnitNormal[1]*delta_vel[0]-UnitNormal[0]*delta_vel[1];

In 3D, the first three columns of the eigenvector matrix used by SU2 ($j = x, y, z$) are

$$P_j = n_j \begin{pmatrix} 1 \\ \mathbf{u} \\ q^2/2 \end{pmatrix} + \rho \begin{pmatrix} 0 \\ \mathbf{n}\times\mathbf{e}_j \\ \mathbf{u}\cdot(\mathbf{n}\times\mathbf{e}_j) \end{pmatrix}$$

so their wave strengths must be

$$\alpha_j = n_j\left(\Delta\rho - \frac{\Delta p}{c^2}\right) + (\Delta\mathbf{u}\times\mathbf{n})_j .$$

With these, $\sum_j \alpha_j P_j$ is exactly the entropy wave plus the shear wave, $\left(\Delta\rho - \Delta p/c^2\right)(1, \mathbf{u}, q^2/2) + \rho,(0, \Delta\mathbf{u}_t, \mathbf{u}\cdot\Delta\mathbf{u}_t)$, where $\Delta\mathbf{u}_t$ is the tangential part of the velocity jump. The three schemes used $\alpha_x = \Delta\rho - \Delta p/c^2$, $\alpha_y = (\Delta\mathbf{u}\times\mathbf{n})_y$, $\alpha_z = (\Delta\mathbf{u}\times\mathbf{n})_z$, which is right only when $\mathbf{n} = \mathbf{e}_x$. This is the standard 3D Roe dissipation (Roe 1981; Blazek 2015). L2Roe and LMRoe keep their low-Mach scaling of the velocity jumps (Oßwald et al. 2016; Rieper 2011).

• General-gas Roe, protection for non-physical states. When the averaged speed of sound is not valid, the scheme should set the whole Jacobian to zero. Because of a wrong loop index it cleared only the diagonal, and the rest kept the values of the previous face.

  SU2/SU2_CFD/src/numerics/flow/convection/roe.cpp

  Lines 811 to 816 in a6b7496

  	for (iVar = 0; iVar < nVar; iVar++) {
  	Flux[iVar] = 0.0;
  	for (jVar = 0; jVar < nVar; jVar++) {
  	Jacobian_i[iVar][iVar] = 0.0;
  	Jacobian_j[iVar][iVar] = 0.0;
  	}

A new unit test checks that a contact and a shear layer give the correct (upwind) flux in 2D and 3D for all four Roe variants. Without the fix, 50 of its checks fail.

This PR builds on #2943. It is part of the split of #2941.

References

• P. L. Roe, Approximate Riemann solvers, parameter vectors, and difference schemes, J. Comput. Phys. 43 (1981) 357–372.
• J. Blazek, Computational Fluid Dynamics: Principles and Applications, 3rd ed., Butterworth-Heinemann, 2015 (Roe scheme).
• F. Rieper, A low-Mach number fix for Roe's approximate Riemann solver, J. Comput. Phys. 230 (2011) 5263–5287 (LMRoe).
• K. Oßwald, A. Siegmund, P. Birken, V. Hannemann, A. Meister, L2Roe: a low dissipation version of Roe's approximate Riemann solver for low Mach numbers, Int. J. Numer. Methods Fluids 81 (2016) 71–86.

Related Work

• Consistent calculation of dissipation terms for Roe #299: the standard Roe scheme with the full 3D dissipation.
• Fix mean-flow solver bugs: under-relaxation, HLLC on moving grids, moving-grid Jacobians and others #2941 (split).

PR Checklist

• I am submitting my contribution to the develop branch.
• My contribution generates no new compiler warnings (try with --warnlevel=3 when using meson).
• My contribution is commented and consistent with SU2 style (https://su2code.github.io/docs_v7/Style-Guide/).
• I used the pre-commit hook to prevent dirty commits and used pre-commit run --all to format old commits.
• I have added a test case that demonstrates my contribution, if necessary.
• I have updated appropriate documentation (Tutorials, Docs Page, config_template.cpp), if necessary.

🤖 Generated with Claude Code

https://claude.ai/code/session_01LEL91DW5WPbPwgFtCvHga6

[joshkellyjak]

const auto

[joshkellyjak]

same here

[joshkellyjak]

^

[rois1995]

Merged the updated #2943 in 73af49d to propagate the latest #2942/develop changes through the stack.

[rois1995]

Propagated the ideal-gas HLLC supersonic face-enthalpy Jacobian fix and the regression test covering both Jacobian modes from #2943 (4960dd03be). The HLLC unit tests pass with 784 assertions. The convergence comparison and its scope are documented in #2943.