Low Mach Asymptotic Preserving Scheme for the Euler-Korteweg Model

Abstract

We present an all speed scheme for the Euler-Korteweg model. We study a semi-implicit time-discretisation which treats the terms, which are stiff for low Mach numbers, implicitly and thereby avoids a dependence of the timestep restriction on the Mach number. Based on this we present a fully discrete finite difference scheme. In particular, the scheme is asymptotic preserving, i.e., it converges to a stable discretisation of the incompressible limit of the Euler-Korteweg model when the Mach number tends to zero.

References in corpus (2)

• Fast and Accurate Coarsening Simulation with an Unconditionally Stable Time Step
• Energy consistent DG methods for the Navier-Stokes-Korteweg system

Cited by in corpus (2)

• Reduced relative entropy techniques for a priori analysis of multiphase problems in elastodynamics
• Reduced relative entropy techniques for a posteriori analysis of multiphase problems in elastodynamics