Entropy Splitting for High Order Numerical Simulation of Compressible Turbulence

• Authors: N. D. Sandham;H. C. Yee
• Venue: Entropy Splitting for High Order Numerical Simulation of Compressible Turbulence
• Year: 2000

A stable high order numerical scheme for direct numerical simulation (DNS) of shock-free compressible turbulence is presented. The method is applicable to general geometries. It contains no upwinding, artificial dissipation, or filtering. Instead the method relies on the stabilizing mechanisms of an appropriate conditioning of the governing equations and the use of compatible spatial difference operators for the interior points (interior scheme) as well as the boundary points (boundary scheme). An entropy splitting approach splits the inviscid flux derivatives into conservative and non-conservative portions. The spatial difference operators satisfy a summation by parts condition leading to a stable scheme (combined interior and boundary schemes) for the initial boundary value problem using a generalized energy estimate. A Laplacian formulation of the viscous and heat conduction terms on the right hand side of the Navier-Stokes equations is used to ensure that any tendency to odd-even decoupling associated with central schemes can be countered by the fluid viscosity. A special formulation of the continuity equation is used, based on similar arguments. The resulting methods are able to minimize spurious high frequency oscillation producing nonlinear instability associated with pure central schemes, especially for long time integration simulation such as DNS. For validation purposes, the methods are tested in a DNS of wall bounded compressible turbulent plane channel flow at a friction Mach number of 0.1 where a very accurate turbulence data base exists. It is demonstrated that the methods are robust in terms of grid resolution, and in good agreement with incompressible channel data, as expected at this Mach number. Accurate turbulence statistics can be obtained with moderate grid sizes. Stability limits on the range of the splitting parameter are determined from numerical tests.