A Skew-Symmetric Energy Stable Almost Dissipation Free Formulation of the Compressible Navier-Stokes Equations

Abstract

We show that a specific skew-symmetric formulation of the nonlinear terms in the compressible Navier-Stokes equations leads to an energy rate in terms of surface integrals only. No dissipative volume integrals contribute to the energy rate. We also discuss boundary conditions that bounds the surface integrals.