Implicit large eddy simulation for unsteady multi-component compressible turbulent flows

Numerical methods for the simulation of shock-induced turb ulent mixing have been investigated, focussing on Implicit Large Eddy Simulation . Shock-induced turbulent mixing is of particular importance for many astrophysical p henomena, inertial confinement fusion, and mixing in supersonic combustion. These dis cipl nes are particularly reliant on numerical simulation, as the extreme nature of th e flow in question makes gathering accurate experimental data di fficult or impossible. A detailed quantitative study of homogeneous decaying turb ulence demonstrates that existing state of the art methods represent the growth of tur bulent structures and the decay of turbulent kinetic energy to a reasonable degree of acc ur y. However, a key observation is that the numerical methods are too dissipative high wavenumbers (short wavelengths relative to the grid spacing). A theoretical an alysis of the dissipation of kinetic energy in low Mach number flows shows that the leading order dissipation rate for Godunov-type schemes is proportional to the speed of sou nd and the velocity jump across the cell interface squared. This shows that the dissi pation of Godunov-type schemes becomes large for low Mach flow features, hence imped ng the development of fluid instabilities, and causing overly dissipative turb lent kinetic energy spectra. It is shown that this leading order term can be removed by loca lly modifying the reconstruction of the velocity components. As the modificatio n is local, it allows the accurate simulation of mixed compressible /incompressible flows without changing the formulation of the governing equations. In principle, the m odification is applicable to any finite volume compressible method which includes a recon struction stage. Extensive numerical tests show great improvements in performanc e t low Mach compared to the standard scheme, significantly improving turbulent k i etic energy spectra, and giving the correct Mach squared scaling of pressure and dens ity variations down to Mach 10−4. The proposed modification does not significantly a ffect the shock capturing ability of the numerical scheme. The modified numerical method is validated through simulati ons of compressible, deep, open cavity flow where excellent results are gained wit h m nimal modelling effort. Simulations of single and multimode Richtmyer-Meshkov instability show that the modification gives equivalent results to the standard sc heme at twice the grid resolution in each direction. This is equivalent to sixteen time s d crease in computational time for a given quality of results. Finally, simulations of a shock-induced turbulent mixing experiment show excellent qualitative agreement wi th available experimental data.