A flux correction approach for the pressure equation in incompressible flows on overset meshes in OpenFOAM

Standard interpolation methods between overset meshes in finite-volume methods such as distance-weighted or least squares based methods do not respect the conservation property of the finite-volume method. As the resultant fluxes exchanged between meshes do not vanish on a global scale, there is either a source or sink in the mass, momentum or energy. This then manifests itself as reduced order of accuracy in the flow variables such as velocity and pressure or high amplitude oscillations in the pressure field when the mesh moves. For incompressible flows, the pressure Poisson equation unanimously decides the extent to which mass is conserved. In this paper, the pressure Poisson equation is isolated and analyzed independently to understand the source of the conservation error. Based on the discretized pressure Poisson equation, a novel flux correction method applicable to moving overset meshes is derived. Using exact solutions for the pressure Poisson equation, it is shown that this method improves the order of accuracy and the discretization error and reduces the mass conservation error. An order of magnitude reduction in the oscillations of the pressure field is also observed when the mesh moves.