Artificial viscosity to get both robustness and discrete entropy inequalities

Christophe Berthon , Manuel J. Castro Díaz , Arnaud Duran (1, 2) , Tomás Morales de Luna , Khaled Saleh

1 ICJ - Institut Camille Jordan
2 MMCS - Modélisation mathématique, calcul scientifique

In the present work, we consider the numerical approximation of the weak solutions of first-order system of evolution laws supplemented with entropy inequalities. The systems under consideration are hyperbolic as soon as a conservation form is satisfied, but such stability property may be lost for non-conservative systems. Here, we show that the robustness and the entropy stability of any finite volume numerical scheme can be restored by introducing a suitable artificial numerical viscosity.

Mots clés: Evolution laws; finite volume schemes; CFL-like condition; robustness; discrete entropy inequalities

Domaines: Mécanique des fluides [physics.class-ph]; Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]; Analyse numérique [math.NA]

Christophe Berthon, Manuel J. Castro Díaz, Arnaud Duran, Tomás Morales de Luna, Khaled Saleh. Artificial viscosity to get both robustness and discrete entropy inequalities. 2022. ⟨hal-03825658⟩