Numerical simulations of jump discontinuity solutions for compressible Stokes flows

Abstract

It has been shown in [8] that the solutions of compressible Stokes flows with inflow jump condition can be decomposed into the jump discontinuity part (due to the pressure jump) plus the contact singularity (to the boundary) plus the smoother one, which is twice differentiable. In this paper we design a numerical scheme of each part in the decomposition and numerically demonstrate its essential role for capturing the jump discontinuity behaviors of the solutions. Several numerical simulations are presented, describing the critical role of each part. It is thought that such algorithm is new in constructing the jump discontinuity solutions.