A ghost-cell immersed boundary method on preventing spurious oscillations for incompressible flows with a momentum interpolation method

Abstract

We propose a ghost-cell immersed boundary method (GCIBM) using a local directional ghost cell approach for the simulation of incompressible flows involving solid geometry. The proposed method is based on a finite volume solver with a momentum interpolation method (MIM) on a collocated grid for the Navier-Stokes equations that is spatially discretized by a fourth-order compact scheme and temporally advanced by a fourth-order Runge-Kutta scheme. A new stencil for imposing the Neumann boundary is constructed following the least square regression. The spurious oscillations that spread from the immersed boundary are observed when the discrete momentum forcing (DMF) is obtained at the cell centers for velocities. This is due to the decoupling of the pressure and velocity fields. In this paper, the spurious oscillations are removed by the recovery of the decoupling by shifting the locations of DMF from the cell centers to the face centers. The efficiency of the proposed technique is confirmed in terms of a simulation for steady and unsteady flows with a stationary or moving geometry.