Numerical computation of three-dimensional incompressible Navier-Stokes equations in primitive variable form by DQ method

In this paper, the global method of differential quadrature (DQ) is applied to solve three-dimensional Navier-Stokes equations in primitive variable form on a non-staggered grid. Two numerical approaches were proposed in this work, which are based on the pressure correction process with DQ discretization. The essence in these approaches is the requirement that the continuity equation must be satisfied on the boundary. Meanwhile, suitable boundary condition for pressure correction equation was recommended. Through a test problem of three-dimensional driven cavity flow, the performance of two approaches was comparatively studied in terms of the accuracy. The numerical results were obtained for Reynolds numbers of 100, 200, 400 and 1000. The present results were compared well with available data in the literature. In this work, the grid-dependence study was done, and the benchmark solutions for the velocity profiles along the vertical and horizontal centrelines were given.