Computation of incompressible Navier-Stokes equations by local RBF-based differential quadrature method

Abstract

Local radial basis function-based differential quadrature (RBF-DQ) method was recently proposed by us. The method is a natural mesh-free approach. It can be regarded as a combination of the conventional differential quadrature (DQ) method with the radial basis functions (RBFs) by means of taking the RBFs as the trial functions in the DQ scheme. With the computed weighting coefficients, the method works in a very similar fashion as conventional finite difference schemes. In this paper, we mainly concentrate on the applications of the method to incompressible flows in the steady and unsteady regions. The multiquadric (MQ) radial basis functions are chosen in this study for their exponential convergence. Three two-dimensional cases are tested, and they are the driven-cavity flow, flow past one isolated cylinder at moderate Re number, and flow around two staggered circular cylinders. Excellent numerical results are obtained. The success of these numerical simulations indicates the flexibility and good performance of the method in simulating incompressible flow with geometrical and dynamic complexity. Copyright © 2005 Tech Science Press.