Directional artificial fluid properties for compressible large-eddy simulation

Abstract

An improved methodology for large-eddy simulation (LES) for flows involving shock waves and turbulence is described. This approach provides better shock capturing and enhanced resolution of turbulence while preserving numerical stability on high aspect ratio (AR) grids. The proposed improvements are based on the LES approach which uses artificial fluid diffusivities (shear viscosity, bulk viscosity and thermal diffusivity) to damp the unresolved gradients of turbulence, shock waves and contact discontinuities, respectively. The scalar artificial viscosities are active only in under-resolved regions of the flow and added directly to the physical quantities. On high aspect ratio grids, the length scale disparity of the mesh leads to over dissipation in one or more direction, causing mis-prediction of physical quantities and added numerical stiffness which reduces the stable time step by a factor of 1/AR. Our proposed method allows fluid diffusivities to be independently applied along each grid direction by forming directional quantities, which ensure the method is minimally dissipative. This alternative approach reduces the errors and numerical stiffness associated with over dissipation. Several test cases are presented which demonstrate the improved performance of this approach on high aspect ratio grids and the enhanced numerical stability. Brief results from LES of an over-expanded planar nozzle are given which demonstrate the method’s robustness on practical applications.