Wall-modeled large eddy simulations using the volume-filtering framework

Abstract

In the present paper, we apply the framework of volume filtering, initially proposed by [T. B. Anderson and R. Jackson, Ind. Eng. Chem. Fundam. 6, 524 (1967)10.1021/i160024a007] for particle-laden flows, to large eddy simulations (LES) of wall-bounded flows leading to a new perspective on wall-modeled LES (WMLES) that we refer to as volume-filtered WMLES (VF-WMLES). In contrast to existing wall models, the VF-WMLES framework does not rely on temporal averaging, does not make a priori assumptions on the pressure gradient, and can be used with a uniform spatial filter, which avoids the appearance of commutation closures in spatial derivatives of the filtered momentum and continuity equation. Volume filtering is well defined, even close to the wall, and it is shown that a nonzero slip and penetration velocity at the wall is a direct consequence of volume filtering the flow. With the VF-WMLES concept, new wall models can be directly assessed in a priori and a posteriori studies by comparing the predicted slip and penetration velocities at the wall with the velocities from explicitly volume-filtered direct numerical simulations (DNS). Based on the VF-WMLES concept, we derive an LES modeling strategy that is based on the recently proposed physically consistent immersed boundary method [M. Hausmann, J. Comput. Phys. 519, 113448 (2024)0021-999110.1016/j.jcp.2024.113448], a modeling framework based on volume filtering allowing to couple the flow with arbitrarily shaped solid boundaries using relatively coarse Cartesian fluid meshes. The proposed VF-WMLES is validated with two cases, a turbulent channel flow and a turbulent flow over periodic hills, and we show it accurately predicts the wall-boundary conditions known from explicitly volume-filtered DNS.