A non-equilibrium slip wall model for large-eddy simulation with an immersed boundary method

Abstract

A non-equilibrium wall model for large-eddy simulation with the immersed boundary (IB) method is proposed to reduce the required number of grid points in simulating wall-bounded turbulence. The proposed wall model is presented as an appropriate slip velocity on the wall. The slip velocity is constructed by integrating the simplified turbulent boundary layer (TBL) equation along the wall-normal direction, which enhances the integral momentum balance near the wall on a coarse grid. The effect of pressure gradient on the near wall flow is taken into account by retaining the pressure gradient term in the simplified TBL equation. The proposed model is implemented in the form of a direct-forcing IB method with moving-least-square reconstruction near the wall. The benchmarks of plane channel turbulence and the flows over a backward-facing step are used for validation. The proposed model improves the wall stresses and velocity profiles in the region where the pressure gradient dominates the near wall flows.