Monotone integrated large eddy simulation of supersonic boundary layer flows

Abstract

For simulations of supersonic flows shock-capturing schemes have to be used. A shock-capturing scheme produces more dissipation than a central difference scheme. In fact, the numerical dissipation produced by shock-capturing schemes is problematic when performing Large Eddy Simulation of supersonic flows with shock-waves. Another train of thought is to turn the numerical dissipation to our advantage. If the numerical dissipation of a numerical method can mimic the dissipation of the subgrid-scale(SGS) eddies, not only is SGS modelling unnecessary, but the numerical dissipation will be a positive contribution to the calculation. This approach is called MILES. As a reference case, a zero-pressure-gradient, flat-plate boundary-layer flow was chosen as there are analytical, experimental, DNS and LES results available. The freestream conditions are a Mach number of 2.25 and a Reynolds number of 1.613 x 104/in or 6.007 x 103 based on the displacement thickness. The central difference scheme, Osher’s scheme and Roe’s scheme are tested for suitability in MILES. The central difference scheme is found to be numerically^ too non-dissipative without SGS modelling. Osher’s scheme is too dissipative so that it hinders the development of turbulence. Roe’s scheme without use of a limiter seems to have the right amount of numerical dissipation to mimic a SGS model. Two popular slope limiters were also tested, but both affected turbulence development when no shockwave was present.