Comparative Studies of Three Approaches for GDQ Computation of Incompressible Navier–Stokes Equations in Primitive Variable Form

Abstract

Three numerical approaches for solving the incompressible Navier–Stokes equations in primitive variable form are proposed and compared in this work. All these approaches are based on the SIMPLE strategy with GDQ discretization on a non-staggered grid. It was found that the satisfying of the continuity equation on the boundary is critical to obtain an accurate numerical solution. The proposed three approaches are to make sure that the continuity equation is satisfied on the boundary, and in the meantime, recommend the boundary condition for pressure correction equation. Through a test problem of two-dimensional driven cavity flow, the performance of three approaches is comparatively studied in terms of the efficiency and accuracy. For all three approaches, accurate numerical results can be obtained by using just a few grid points.