A sensor-restrained artificial shear diffusivity for large-eddy simulations of vortex-dominated compressible flows

Abstract

We propose a sensor-restrained model for the shear viscosity term within the localized artificial diffusivity (LAD) scheme to stabilize compressible large-eddy simulations with low-pressure-core vortical structures. LAD methods are used in numerical solvers based on spectral-like compact finite-difference schemes. While high-order-accurate numerical schemes with proper discretization guarantees physical fidelity, the LAD role is to suppress non-physical oscillations arising in compressible flow simulations near shock waves and other sharp gradients. LAD is a cost-effective approach which adds artificial shear and bulk viscosities, and thermal conductivity to their physical counterparts. However, an unrestricted added diffusivity may lead to poorly-resolved coherent structures and undesirable turbulence statistics. In order to prevent excessive numerical diffusion in compressible shear flows, the artificial shear viscosity term can be disabled in cases where the simulation is already stable. However, in flow simulations where vortices emerge within a low-pressure region, a strong pressure decay may lead to instabilities that make the simulation unstable. For such cases, adding artificial shear viscosity is necessary to maintain numerical stability, as this issue is unaddressed by the artificial bulk viscosity and thermal conductivity alone. Our approach integrates a sensor into the standard LAD formulation, particularly in the artificial shear viscosity, that reduces the added diffusivity while preserving numerical stability. This advancement is possible by adding the shear diffusivity only in localized flow regions consisting of low-pressure-core vortices, and it enables stable and accurate large-eddy simulations (LES) of compressible vortex-dominated flows, such as those encountered in separated flows and bluff-body wakes.