Robust Solver for Incompressible Flow on Cartesian Grids with Colocated Variables

摘要

We describe a second-order finite-volume formulation for solving incompressible flow problems on Cartesian grids using a colocated arrangement of variables. A projection method is used, in which a provisional cell-centered velocity is obtained by integrating the effects of advection and viscous forces over the numerical time step. Interface velocities are then interpolated from the provisional cell-centered velocities and corrected using the solution of a Poission equation for the pressure distribution. The cell-centered velocities are then interpolated from the corrected interface velocities. This pair of interpolation steps adds numerical diffusion that mimics a normal viscous stress, and the form of this damping term is similar to that which comes from stabilizing the Poisson equation for pressure by adding a term that is proportional to the fourth-derivative of pressure. The method requires no extra damping terms in order to maintain stability.