Global method for solving incompressible Navier-Stokes equations in the general coordinate system

Abstract

For the efficient numerical solutions of incompressible Navier-Stokes equations in the general coordinate system, this paper applies a global method of generalized differential quadrature (GDQ) to discretize the spatial derivatives, and a first order Euler implicit finite difference scheme to discretize the time derivative. After numerical discretization, the resultant algebraic equations are solved implicitly. The vorticity-stream function formulation was chosen as the governing equations. Numerical results for a smooth expansion channel flow demonstrated that accurate numerical results can be obtained using just a few grid points.