Multiscale Computations for Kinetic and Related Problems

Asymptotic preserving schemes for Euler equations of gas dynamics and shallow water equations with Coriolis forces

Alexander Kurganov

Southern University of Science and Technology and Tulane University

We are interested in deriving robust asymptotic preserving (AP) numerical methods for Euler equations of gas dynamics and shallow water equations with Coriolis forces. It is well-known that both the Euler and shallow water equations become stiff in low Mach and low Froude number regimes, respectively. In these regimes, the applicability of explicit schemes is limited due to severe stability limitation on the mesh size. In order to design substantially more efficient numerical methods, one typically needs to design an AP scheme, which approximates the incompressible equation obtained in the limiting zero Mach/Froude number case. Such schemes can be designed using either a flux splitting implicit-explicit (IMEX) or fully implicit approach. In this talk, I will discuss both approaches and present several different AP schemes.