Mass-conserving ghost cell immersed boundary method with multigrid for coupled Navier-Stokes solvers

Although simple to implement, ghost cell immersed boundary methods in their basic form do not conserve mass globally, even in a mass-conservative finite volume framework where local mass conservation is satisfied in the fluid domain. Reconstruction near solid boundaries with corners is also difficult. Furthermore, when used with coupled solvers on collocated grids, correct implementation of momentum weighted interpolation at the boundaries is not straightforward. The approach presented here overcomes these issues by combining a directional ghost cell method with a weighted face flux correction based on the global mass continuity error. The method is simple to implement and only requires the addition of source terms to the discrete equations. The method is used in a fully coupled FAS multigrid scheme where the immersed boundary is applied on all grid levels. The scheme has been verified and validated for a number of canonical steady incompressible flows, and excellent performance and efficiency is demonstrated with linear scaling with problem size.