Parallel simulation of incompressible viscous flows by generalized differential quadrature

Abstract

The technique of differential quadrature (DQ) for the solution of a partial differential equation is extended and generalized. The general formulation for determining the weighting coefficients of the first order derivative is obtained, and a recurrence relationship for determining the weighting coefficients of the second and higher order partial derivatives is achieved. For parallel computation, the multi-domain GDQ scheme was also developed, and successfully applied to the solution of the incompressible Navier-Stokes (N-S) equations. Numerical examples include the flow past a backward facing step, the flow past a square step, and driven cavity flow. For the driven cavity flow problem, two formulations of the N-S equations (vorticity-stream function and vorticity-velocity) and three methods for dealing with the interface between subdomains (i.e. patched by enforcing continuity to the function and its normal derivative; patched by using a Lagrange interpolation scheme; and overlapped) were studied comparatively. In addition, an attempt to develop a general code which can be run on any array of processors without modification to the program was discussed, and then successfully applied to the driven cavity flow problem.