Direct Numerical Simulations of Compressible Turbulence Using Higher Order Method of Lines

Abstract

The compressible turbulence plays an important role in the scientific and engineering phenomena, e.g., the re-entry into the atmosphere of vehicles, the scramjets, the high temperature plasmas and the combustion. However, the exquisite compressible turbulent model has not yet been devised. Therefore, the direct numerical simulations (DNS) of the compressible turbulence have a very important aspect. The DNS of the homogeneous compressible turbulence has been reported[1–4]. As everybody knows, the higher order method is necessary to solve the turbulent flows directly. In this paper, we devise the higher order method of lines[5] for the DNS of the compressible turbulence. The higher order method of lines consists of the spatial discretization and the time integration. The spatial derivatives of the partial differential equations (PDEs) in space and time, i.e., the compressible Navier-Stokes equations, are discretized by the modified differential quadrature (MDQ) method[6]. The resulting system of the ordinary differential equations (ODEs) in time is integrated by the low storage Runge-Kutta (LSRK) scheme proposed by Williamson[7].