[petsc-users] FEM SUPG gmres

Wed May 27 06:47:52 CDT 2026

Hello!

I am developing a conservative variable steady-state compressible RANS 
(Spalart Allmaras) solver in FENICSX with SUPG stabilisation. My aim is 
to solve 3D flows around Mach numbers of approximately 0.4 at Re~1*10^6 
in duct. My boundary conditions are implemented using flux (no strong 
dirichlet)

At the moment, I am using a pseudo-transient continuation (PTC) 
algorithm where the Jacobian contains a time term but the residual is 
stationary. I am  using a snes solver with FGMRES preconditioned by ASM 
+ ILU(2) (rtol = 0.1, restart = 300, modifiedgradshmidt,  rcm ordering, 
overlap 2, restrictive ASM, ). I solve 1 Newton iteration then modify 
the CFL ... However, as my CFL increases (before and close to quadratic 
convergence), I observe a marked deterioration in performance, and the 
solver requires >200 iterations to reach the FGMRES’s rtol of 0.1. In 
some complex cases (S shaped suct with flow separation), even 600 
iterations are insufficient.

I have also noticed that some Newton iterations strangely take an 
extremely long time to complete, despite a constant or similar number of 
ILU iterations, and the only way I have found to fix this is to enable 
diagonal scaling (and the fix). In this case, the time taken to solve 
the problem is ‘logical’, and only increases as the number of iterations 
in the GMRES increases. You will find an example of this phenomenon 
attached (residual.txt). I’ve checked the time to compute the Jacobian 
and the residual, and that’s not where the problem lies.

Do you think that Non-dimensionalization my variables could help GMRES 
converge more effectively ? Because, in fact, there are significant 
differences in the order of magnitude of the L2 residuals for each 
equation. Is using diagonal scaling sufficient?

I would like to be able to optimise this solver to limit the number of 
iterations required for the FGMRES to converge; are there any PETSc 
options I haven’t considered? I have also noticed that FUN3D, for 
example, solves the equations in primitive variables (rho,v,T,nu_tilde); 
could this improve the convergence of the system?

Thank you for any help or ideas!

-- 
*Nathan Langlet*
Etudiant doctorant
Département aérodynamique, aéroélasticité, acoustique
MASH
Tél: +33 1 46 23 51 61

ONERA - The French Aerospace Lab - Centre de Meudon
8, rue des Vertugadins - 92190 MEUDON
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Iteration  11 | Résidu L2: 3.056e-02 CFL: 1.16
Résidus L2 rel: ‖ρ‖₂ = 3.827e-02, ‖ρv‖₂ = 2.127e-02, ‖ρE‖₂ = 3.056e-02, ‖ρν‖₂ = 8.434e-03
Résidus L2 abs: ‖ρ‖₂ = 1.252e-04, ‖ρv‖₂ = 1.486e-01, ‖ρE‖₂ = 3.815e+01, ‖ρν‖₂ = 1.265e-07
Temps assemblage J:  8.5449378490448
    Linear ns_ solve converged due to CONVERGED_RTOL iterations 4
temps écoulé_solve: 20.20 s
------------------------------------------------------------
Iteration  12 | Résidu L2: 2.707e-02 CFL: 1.46
Résidus L2 rel: ‖ρ‖₂ = 3.389e-02, ‖ρv‖₂ = 1.820e-02, ‖ρE‖₂ = 2.707e-02, ‖ρν‖₂ = 7.252e-03
Résidus L2 abs: ‖ρ‖₂ = 1.109e-04, ‖ρv‖₂ = 1.271e-01, ‖ρE‖₂ = 3.379e+01, ‖ρν‖₂ = 1.087e-07
Temps assemblage J:  8.567534923553467
    Linear ns_ solve converged due to CONVERGED_RTOL iterations 4
temps écoulé_solve: 20.33 s
------------------------------------------------------------
Iteration  13 | Résidu L2: 2.398e-02 CFL: 1.82
Résidus L2 rel: ‖ρ‖₂ = 3.000e-02, ‖ρv‖₂ = 1.567e-02, ‖ρE‖₂ = 2.398e-02, ‖ρν‖₂ = 6.346e-03
Résidus L2 abs: ‖ρ‖₂ = 9.815e-05, ‖ρv‖₂ = 1.095e-01, ‖ρE‖₂ = 2.993e+01, ‖ρν‖₂ = 9.516e-08
Temps assemblage J:  8.53394341468811
    Linear ns_ solve converged due to CONVERGED_RTOL iterations 4
temps écoulé_solve: 45.62 s
------------------------------------------------------------
Iteration  14 | Résidu L2: 2.122e-02 CFL: 2.27
Résidus L2 rel: ‖ρ‖₂ = 2.652e-02, ‖ρv‖₂ = 1.357e-02, ‖ρE‖₂ = 2.122e-02, ‖ρν‖₂ = 5.785e-03
Résidus L2 abs: ‖ρ‖₂ = 8.677e-05, ‖ρv‖₂ = 9.483e-02, ‖ρE‖₂ = 2.649e+01, ‖ρν‖₂ = 8.674e-08
Temps assemblage J:  8.560238122940063
    Linear ns_ solve converged due to CONVERGED_RTOL iterations 5
temps écoulé_solve: 38.83 s
------------------------------------------------------------
Iteration  15 | Résidu L2: 1.864e-02 CFL: 2.84
Résidus L2 rel: ‖ρ‖₂ = 2.328e-02, ‖ρv‖₂ = 1.181e-02, ‖ρE‖₂ = 1.864e-02, ‖ρν‖₂ = 5.521e-03
Résidus L2 abs: ‖ρ‖₂ = 7.616e-05, ‖ρv‖₂ = 8.247e-02, ‖ρE‖₂ = 2.326e+01, ‖ρν‖₂ = 8.280e-08
Temps assemblage J:  8.55243706703186
    Linear ns_ solve converged due to CONVERGED_RTOL iterations 5
temps écoulé_solve: 34.65 s
------------------------------------------------------------
Iteration  16 | Résidu L2: 1.626e-02 CFL: 3.55
Résidus L2 rel: ‖ρ‖₂ = 2.030e-02, ‖ρv‖₂ = 1.030e-02, ‖ρE‖₂ = 1.626e-02, ‖ρν‖₂ = 5.436e-03
Résidus L2 abs: ‖ρ‖₂ = 6.643e-05, ‖ρv‖₂ = 7.196e-02, ‖ρE‖₂ = 2.030e+01, ‖ρν‖₂ = 8.152e-08
Temps assemblage J:  8.529710054397583
    Linear ns_ solve converged due to CONVERGED_RTOL iterations 6
temps écoulé_solve: 53.96 s