Numerical investigations of the compressible Navier-Stokes system

In this paper we write, analyze and experimentally compare three different numerical schemes dedicated to the one dimensional barotropic Navier-Stokes equations: a staggered scheme based on Rusanov for inviscid (Euler) system, pseudo-Lagrangian in which mesh “follows” fluid, Eulerian projection (on fixed mesh) of preceding scheme. All these only involve resolution linear systems (all nonlinear terms are solved an explicit way). We propose illustrations their behaviors particular solutions density has discontinuities (hereafter called Hoff solutions). show that seem converge same solutions, evolution amplitude discontinuity solution (with scheme) with predicted by observe good agreement.