Universität Freiburg

Compressible Navier-Stokes Equations

© Aleksandra Egelja


The conservation of mass, momentum and energy of a nonstationary compressible viscous flow is described through the Navier-Stokes equation of gas dynamic. These equation are given in conservative form:

Finite Volume Method


We discretize the system of the compressible Navier-Stokes equations by an explicit first order finite volume scheme with a suitable Riemann solver for the convective terms. The finite volume scheme for this system can be written as:

AUSMDV Riemann solver

A flux splitting scheme (AUSMDV) is recognized as an improved advection upstream splitting method (AUSM) by Liou and Steffen. The AUSMDV is a mixture of AUSMD and AUSMV, which will be defined in the following.