Upwind local differential quadrature method for solving incompressible viscous flow Original Research Article

The differential quadrature method (DQM) is able to obtain quite accurate numerical solutions of differential equations with few grid points and less computational effort. The successful applications of DQM have been reported to solve various problems of fluid mechanics. But, owing to the limitation of its quadrature rules, DQM is convenient only for regular regions and lacks upwind mechanism to characterize the convection of the fluid flow. In the present paper, a local differential quadrature method (LDQM) with upwind mechanism is proposed to solve incompressible viscous fluid flow problems in irregular regions. As its application, planar contraction flows in irregular regions is numerically solved and excellent numerical results are obtained for coarse meshes.