Numerical methods for the simulation of shock-induced turbulent mixing have beeninvestigated, focussing on Implicit Large Eddy Simulation. Shock-induced turbulentmixing is of particular importance for many astrophysical phenomena, inertial confinementfusion, and mixing in supersonic combustion. These disciplines are particularlyreliant on numerical simulation, as the extreme nature of the flow in question makesgathering accurate experimental data difficult or impossible.A detailed quantitative study of homogeneous decaying turbulence demonstrates thatexisting state of the art methods represent the growth of turbulent structures and the decayof turbulent kinetic energy to a reasonable degree of accuracy. However, a key observationis that the numerical methods are too dissipative at high wavenumbers (shortwavelengths relative to the grid spacing). A theoretical analysis of the dissipation ofkinetic energy in low Mach number flows shows that the leading order dissipation ratefor Godunov-type schemes is proportional to the speed of sound and the velocity jumpacross the cell interface squared. This shows that the dissipation of Godunov-typeschemes becomes large for low Mach flow features, hence impeding the developmentof fluid instabilities, and causing overly dissipative turbulent kinetic energy spectra.It is shown that this leading order term can be removed by locally modifying the reconstructionof the velocity components. As the modification is local, it allows theaccurate simulation of mixed compressible/incompressible flows without changing theformulation of the governing equations. In principle, the modification is applicable toany finite volume compressible method which includes a reconstruction stage. Extensivenumerical tests show great improvements in performance at low Mach comparedto the standard scheme, significantly improving turbulent kinetic energy spectra, andgiving the correct Mach squared scaling of pressure and density variations down toMach 10−4. The proposed modification does not significantly affect the shock capturingability of the numerical scheme.The modified numerical method is validated through simulations of compressible,deep, open cavity flow where excellent results are gained with minimal modellingeffort. Simulations of single and multimode Richtmyer-Meshkov instability show thatthe modification gives equivalent results to the standard scheme at twice the grid resolutionin each direction. This is equivalent to sixteen times decrease in computationaltime for a given quality of results. Finally, simulations of a shock-induced turbulentmixing experiment show excellent qualitative agreement with available experimentaldata.
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