Force-amplified, single-sided diffused-interface immersed boundary kernel for correct local velocity gradient computation and accurate no-slip boundary enforcement

The current diffused-interface immersed boundary method (IBM) with a two-sided force distribution kernel cannot be used to correctly calculate the velocity gradients within the diffused solid-fluid interfaces. This is because the nonzero boundary force distributed to the fluid nodes modifies the momentum equation solved at these locations from the Navier-Stokes equations (NSEs). In this paper, this problem is analytically identified in simple plane channel flow. A single-sided force distribution kernel is used to restrict the boundary force in the solid region and restore NSEs in the fluid region for correct velocity gradient computation. In order to improve the no-slip boundary enforcement in IBM, an extremely simple force amplification technique is proposed. This technique requires no additional computation cost and can significantly reduce the necessary iterations to achieve accurate no-slip boundary enforcement. The single-sided kernel and the force amplification technique are examined in both laminar and turbulent flows. Compared to the standard IBM, the proposed methods not only produce correct velocity gradient results near a solid surface but also reduce numerical errors in the flow velocity and hydrodynamic force and torque results.