A solution for the odd–even decoupling problem in pressure-correction algorithms for variable density flows

When the Navier–Stokes equations are solved on a colocated mesh, a spurious mode for the pressure can appear if no special attention is paid to the discretization of the pressure. This pressure mode can be suppressed by a pressure-weighted interpolation formula for the mass flux over a cell-face. In this paper, a similar cure is presented in the framework of pressure-correction methods in variable density flow. Special attention is given to the solvability condition for the resulting Poisson-like equation for the pressure. It consists of two remedies: a correction term for the cell-face velocity is introduced and the stencil for the discrete Laplacian is compacted. We finally show the applicability of the method on general curvilinear coordinate systems in three dimensions.