Pressure Gradient method for solving incompressible Navier-Stokes equations with curvilinear coordinate system

Abstract

A nonstaggered Pressure Gradient (PG) method, one of the finite difference schemes using primitive variables, is applied to solve the 3-D, unsteady incompressible Navier-Stokes equations based on a curvilinear coordinate system. The PG method, in contrast to conventional methods, uses pressure gradient instead of pressure as the field variable. The most prominent contribution of this method is its adoption of a modified nonstaggered grid which eliminates the troublesome calculation of the pressure boundary conditions and any special treatment for velocities near the boundary. Another advantage is that the discretization error of the convection terms is relatively insensitive to the magnitude of the convecting flow in the high Reynolds number cases. A variety of test problems have been studied, including Couette flow, flow past a cylinder, transient buoyancy convection, and 3-D unsteady cavity flow driven by shear and body forces. The comparisons between the present numerical results and the existing data are shown to be in good agreement.