A mixture differential quadrature method for solving two-dimensional incompressible Navier-Stokes equations

Differential quadrature method (DQM) is able to obtain highly accurate numerical solutions of differential equations just using a few grid points. But using purely differential quadrature method, good numerical solutions of two-dimensional incompressible Navier-Stokes equations can be obtained only for low Reynolds number flow and numerical solutions will not be convergent for high Reynolds number flow. For this reason, in this paper a combinative predicting-correcting numerical scheme for solving two-dimensional incompressible Navier-Stokes equations is presented by mixing upwind difference method into differential quadrature one. Using this scheme and pseudo-time-dependent algorithm, numerical solutions of high Reynolds number flow are obtained with only a few grid points. For example, 1∶1 and 1∶2 driven cavity flows are calculated and good numerical solutions are obtained.