Chapter 12 - Numerical treatment of compressible turbulent flows

Abstract

DNS/LES of compressible turbulent flows is challenged by the nonlinear numerical instabilities that arise at high Reynolds number, the existence of supersonic and highly subsonic regions, and unsteady shock waves. This chapter discusses solutions to these challenges from the author's perspective to simulate complex flows with fidelity comparable to that of canonical flows. A numerical algorithm for compressible turbulence is discussed in which the discrete equations reduce to the incompressible equations at low Mach numbers, and the discretization conserves kinetic energy in the inviscid incompressible limit. Illustrative examples are shown along with details of the formulation. A characteristic-filtering methodology for shock capturing is presented for unstructured grids. The filter is implemented in a predictor–corrector formulation and can be combined with several different base schemes. Examples are shown of capturing strong shock waves in a Fourier pseudospectral code, using a conservative, nondissipative predictor step on unstructured grids, and using a non-conservative, nondissipative predictor step. Finally, these ideas are extended to nonideal gases and fluid mixtures, to simulate multiphase cavitating flows on unstructured grids.