Short Note: 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.

[1]  W. Cabot,et al.  A high-wavenumber viscosity for high-resolution numerical methods , 2004 .

[2]  J. Smagorinsky,et al.  GENERAL CIRCULATION EXPERIMENTS WITH THE PRIMITIVE EQUATIONS , 1963 .

[3]  D. Pullin,et al.  A vortex-based subgrid stress model for large-eddy simulation , 1997 .

[4]  P. Moin,et al.  A dynamic subgrid‐scale model for compressible turbulence and scalar transport , 1991 .

[5]  Nikolaus A. Adams,et al.  A Subgrid-Scale Deconvolution Approach for Shock Capturing , 2002 .

[6]  George Em Karniadakis,et al.  A Spectral Vanishing Viscosity Method for Large-Eddy Simulations , 2000 .

[7]  S. Lele.  Compact finite difference schemes with spectral-like resolution , 1992 .

[8]  S. Corrsin,et al.  The use of a contraction to improve the isotropy of grid-generated turbulence , 1966, Journal of Fluid Mechanics.

[9]  C. Tam,et al.  A Study of the Short Wave Components in Computational Acoustics , 1993 .

[10]  R. D. Richtmyer,et al.  A Method for the Numerical Calculation of Hydrodynamic Shocks , 1950 .

[11]  William J. Rider,et al.  Revisiting Wall Heating , 2000 .

[12]  E. Tadmor,et al.  Convergence of spectral methods for nonlinear conservation laws. Final report , 1989 .

[13]  W. Heisenberg,et al.  Zur statistischen Theorie der Turbulenz , 1948 .

[14]  A. Jameson,et al.  Numerical solution of the Euler equations by finite volume methods using Runge Kutta time stepping schemes , 1981 .

[15]  C. Meneveau,et al.  Decaying turbulence in an active-grid-generated flow and comparisons with large-eddy simulation , 2003, Journal of Fluid Mechanics.

[16]  S. Osher,et al.  Efficient implementation of essentially non-oscillatory shock-capturing schemes,II , 1989 .

[17]  R. Kraichnan.  Eddy Viscosity in Two and Three Dimensions , 1976 .

[18]  S. Corrsin,et al.  Simple Eulerian time correlation of full-and narrow-band velocity signals in grid-generated, ‘isotropic’ turbulence , 1971, Journal of Fluid Mechanics.

[19]  Hervé Jeanmart,et al.  Hyperviscosity and vorticity-based models for subgrid scale modeling , 1997 .

[20]  W. F. Noh.  Errors for calculations of strong shocks using an artificial viscosity and artificial heat flux , 1985 .