Development of a Compact and Accurate Discretization for Incompressible Navier-Stokes Equations Based on an Equation-Solving Solution Gradient, Part III: Fluid Flow Simulations on Staggered Polygonal Grids

Abstract

A compact and accuracy discretization of incompressible Navier-Stokes equations on staggered polygonal grids is presented in this article. It is a sequel to our efforts in developing a feasible solution procedure to simulate incompressible flow problems in complicated domains. By taking advantage of the discretization procedure for the convection-diffusion equation described in our previous work, difference counterparts of the Navier-Stokes equations can be obtained on staggered polygonal grids. Additional ingredients of pressure–velocity coupling and boundary conditions for velocity gradients in the solution procedure are also described. Several test problems are solved to illustrate the feasibility of the present formulation. From the numerical results obtained, it is evident that the proposed scheme is a useful tools to simulate incompressible flow field in arbitrary domains.