Assessment of WENO Methods with Shock-Confining Filtering for LES of Compressible Turbulence

Abstract

Large-eddy simulations (LES) rely on a spatial lter to separate turbulent scales into resolved scales and scales to be modeled, and the majority of modern closure models themselves involve ltering operations. The uniform application of discrete linear lters can create new extrema in the vicinity of o w discontinuities. These new extrema can lead to spurious oscillations and to antiphysical features such as negative pressures. This is similar to the dicult y encountered when using a high-order-accurate linear nite dierence scheme for convective terms in a shock-containing o w. In the case of the convective terms, many shock-capturing methods have been devised to provide physically correct solutions free from spurious oscillations. For example, weighted essentially non-oscillatory (WENO) schemes adapt their numerical stencils in the vicinity of a shock to avoid interpolation across it. In this paper, we propose a \shock-conning lter (SCF) that adapts to avoid ltering across discontinuities. We present a method for constructing an SCF from a general linear lter and assess its performance both in traditional LES models, as exemplied by the dynamic mixed model (DMM), and in mathematical models, as exemplied by the approximate deconvolution model (ADM). Numerical studies of the shocktube problem show that the SCF greatly improves the behavior of the ADM by eliminating spurious oscillations near discontinuities. Simulations of decaying compressible isotropic turbulence show that the SCF gives behavior for the DMM and ADM that is at least comparable to, and in some way better than, the behavior of DMM with linear ltering. Although the best results for the decaying turbulence come from the ADM with relaxation, we do not consider this to be a signican t drawback to the SCF because the SCF enables the ADM to behave qualitatively correctly in o ws where the ADM solution would otherwise exhibit large antiphysical oscillations. Shock-conning ltering in conjunction with ADM improves the prediction of gasdynamics eects without signican tly altering the prediction of turbulence; therefore, we conclude that it holds promise for LES of shock/turbulence interaction problems.