Convective-Difference Scheme Using a General Curvilinear Coordinate Grid for Incompressible Viscous Flow Problems

Abstract

A numerical scheme analyzing unsteady two-dimensional incompressible viscous flow using a general curvilinear coordinate grid is proposed. In this scheme, the unsteady Navier-Stokes equations are solved by a convective-difference scheme using a staggered square grid in transformed space and an interpolation formula considering TVD concept, and an elliptic equation of pressure is solved by the iteration scheme. The continuity condition in the scheme is identically satisfied, and the spurious errors are completely removed, in a manner similar to the MAC scheme. As numerical examples the square cavity, U-type duct and backward-facing step duct flows were calculated. The calculated results show that the scheme has a good accuracy as a second-order scheme and is stable for high Reynolds numbers flow.