A Semi-Implicit All-Mach Numerical Method for Implicit Large Eddy Simulations

Simon D. Wilkinson

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arXiv · 2610.06217

A Semi-Implicit All-Mach Numerical Method for Implicit Large Eddy Simulations

Simon D. Wilkinson

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Abstract

Implicit Large Eddy Simulation (ILES) is a well established approach for modeling high-Reynolds-number turbulent flows by numerical solution of the inviscid Euler equations in 3D. These turbulent flows cover a wide range of Mach numbers, including within individual simulations. For example, Richtmyer-Meshkov instability simulations transition from a high-Mach compressible regime to a low-Mach quasi-incompressible regime during the late-time evolution. These flows motivate the development of a semi-implicit all-Mach numerical method, which is subject to a CFL stability constraint corresponding to the fluid velocity, but independent of the speed of sound, and can be applied efficiently and accurately across the whole spectrum of Mach numbers. Furthermore, finite-volume discretization is chosen to maintain strict conservation and ensure robust and accurate capturing of strong shocks. The method is validated in both high- and low-Mach regimes. Validation is also presented for stratified atmospheres in the presence of gravity, and the method is thus shown to be applicable to buoyancy driven flows. We present favorable comparison against previously published ILES simulations of multimode Richtmyer-Meshkov instability from the $Θ$-group collaboration, Thornber et al., (arXiv:1706.09991).

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Simon D. Wilkinson. 2026-10-05. A Semi-Implicit All-Mach Numerical Method for Implicit Large Eddy Simulations. https://arxiv.org/abs/2610.06217

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