Centered-Potential Regularization for the Advection Upstream Splitting Method

Abstract

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.