Hyperviscosity for shock-turbulence interactions

An artificial viscosity is described, which functions as an effective subgrid-scale model for both high and low Mach number flows. The model employs a bulk viscosity for treating shocks and a shear viscosity for treating turbulence. Each of the viscosities contains an empirical constant; however, the constants do not require adjustment from flow to flow. A polyharmonic operator, applied to the strain rate, imparts spectral-like behavior to the model, thus eliminating the need for ad hoc limiters and/or “dynamic procedures” to turn off the model in smooth regions. The model gives excellent results for Shu’s problem, Noh’s problem and decaying turbulence.