A momentum forcing wall-modeling approach for large eddy simulations with the immersed boundary method

A novel approach is presented for wall-modeled large-eddy simulations with immersed boundaries. In this work, an immersed boundary method (IBM) similar to that proposed by Ghias et al. (2007) was implemented in a GPU-accelerated compressible solver that solves the Navier-Stokes equations in anti-symmetric form using co-located Cartesian grids. An equilibrium wall model function was applied to estimate the wall shear stress in an under-resolved grid. In the current method, an estimate of the contribution of under-resolved wall-normal gradients to the viscous diffusion term is obtained at fluid points near the immersed boundary. The estimate is compared against the diffusion predicted by the wall model function, and the difference between these values is added to the momentum equation as a forcing term acting on the wall-parallel direction. This method avoids directly imposing velocity values at grid points and has the effect of adding momentum in the streamwise direction that would otherwise be lost in the under-resolved flow field. A source term is also applied to the energy equation in a consistent manner to conserve total energy. The method was tested in a turbulent channel flow and other canonical wall-bounded flows.