Modeling the wall-slip in Immersed Boundary Modeled LES

We develop a method to perform wall modeled large eddy simulations (WMLES) compatible with immersed boundary (IB) methods, namely, the volume-filtering immersed boundary (VFIB) method. The ability to decouple complex and possibly moving geometry from the computational domain that IB methods provide allows the use of cartesian grids, which coupled with the favorable grid point scaling requirement of LES, would make simulations of high Reynolds number flows over complex geometries feasible. It has been shown that local grid refinement performed in wall resolved LES (WRLES) introduces unphysical oscillations when using IB methods leaving WMLES as the only means to implement IB methods with LES. In WMLES, it is common to truncate and rescale the filter near boundaries to prevent it from extending out of the fluid domain. This renders the filtering and derivative operators non-commutative, and additional commutation terms arise which are ignored in most WMLES approaches. Unlike traditional WMLES, the VFIB method doesn't require a spatially varying filter kernel as the filter is allowed to extend out of the fluid phase, and a fluid indicator function is introduced to account for both the fluid and solid phases of a flow configuration. While filtering in this way is also not commutative, the commutation terms that arise are carefully tracked to eliminate commutation errors. Along with the commutation terms, volumetric forcing terms arise from filtering boundary conditions, such as the no-slip condition, and these are taken with the commutation terms to form the IB forcing term. The unclosed terms arising from this formulation can be closed via the slip velocity for which we present two models: a volume filtered Van Driest model, and a slip length model. Performance of these models and the behavior of all terms in the VFIB method are evaluated a priori by volume filtering DNS data of turbulent channel flow at friction Reynolds number of 5200.