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In this paper, we introduce a relaxation filtering closure approach toaccount for subgrid scale effects in explicitly filtered large eddy simulationsusing the concept of anisotropic diffusion. We utilize the Perona-Malikdiffusion model and demonstrate its shock capturing ability and spectralperformance for solving the Burgers turbulence problem, which is a simplifiedprototype for more realistic turbulent flows showing the same quadraticnonlinearity. Our numerical assessments present the behavior of variousdiffusivity functions in conjunction with a detailed sensitivity analysis withrespect to the free modeling parameters. In comparison to direct numericalsimulation (DNS) and under-resolved DNS results, we find that the proposedclosure model is efficient in the prevention of energy accumulation at gridcut-off and is also adept at preventing any possible spurious numericaloscillations due to shock formation under the optimal parameter choices. Incontrast to other relaxation filtering approaches, it is also shown that alarger inertial range can be obtained by the proposed anisotropic diffusionmodel using a compact stencil scheme in an efficient way.

An explicit relaxation filtering framework based upon Perona-Malik  anisotropic diffusion for shock capturing and subgrid scale modeling of  Burgers turbulence