Centered-potential regularization for the advection upstream splitting method

Martin Parisot (1) , Jean-Paul Vila (2, 3)

1 ANGE - Numerical Analysis, Geophysics and Ecology
2 IMT - Institut de Mathématiques de Toulouse UMR5219
3 INSA - Institut National des Sciences Appliquées

This paper is devoted to a centered IMEX scheme in a multidimensional framework for a wide class of multicomponent and isentropic flows. The proposed strategy is based on a regularized model where the advection velocity is modified by the gradient of the potential of the conservative forces in both mass and momentum equations. The stability of the scheme is ensured by the dissipation of mechanic energy, which stands for a mathematical entropy, under an advective CFL condition. The main physical properties, such as positivity, conservation of the total momentum, and conservation of the steady state at rest, are satisfied. In addition, asymptotic preserving properties in the regimes (“incompressible” and “acoustic”) are analyzed. Finally, several simulations are presented to illustrate our results in a simplified context of oceanic flows in one dimension.

Mots clés: Hyperbolic conservation laws; well-balanced scheme; entropy dissipation; low-Mach number; low-Froude num-ber; Asymptotic preserving schemes

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]; Dynamique des Fluides [physics.flu-dyn]; Géophysique [physics.geo-ph]; Physique Atmosphérique et Océanique [physics.ao-ph]; Physique mathématique [math-ph]

Martin Parisot, Jean-Paul Vila. Centered-potential regularization for the advection upstream splitting method . SIAM Journal on Numerical Analysis, 2016. ⟨hal-01152395v2⟩