High order difference method on staggered, curvilinear grids for the incompressible Navier-Stokes equations

Abstract

This chapter discusses the high order difference method on staggered, curvilinear grids for the incompressible navier-stokes equations. The incompressible Navier–Stokes equations are solved on a staggered grid. The approximations in space are based on compact 4th order schemes and a semi-implicit second order method is employed for time integration. The resulting system of linear equations in every time step is solved by a combination of outer and inner iterations. The accuracy of the method is verified in the calculation of flow in a constricting channel and in a driven cavity. It develops a high order method for efficient solution of Navier–Stokes' equations in two dimensions. The grids are orthogonal in the physical domain to reduce the number of derivatives in the computational domain; a system of linear equations with a constant matrix is solved in every time step for the unknown variables, the accuracy is of 4th order in space and second order in time.