A 4TH-ORDER ACCURATE METHOD FOR THE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS ON OVERLAPPING GRIDS

A method is described to solve the time-dependent incompressible Navie r-Stokes equations with finite differences on curvilinear overlapping grids in two or three space dimensions. The scheme is fourth-order acc urate in space and uses the momentum equations for the velocity couple d to a Poisson equation for the pressure. The boundary condition for t he pressure is taken as del . u = 0. Extra numerical boundary conditio ns are chosen to make the scheme accurate and stable. The velocity is advanced explicitly in time; any standard time stepping scheme such as Runge-Kutta can be used. The Poisson equation is solved using direct or iterative sparse matrix solvers or by the multigrid algorithm. Comp utational results in two and three space dimensions are given. (C) 199 4 Academic Press, Inc.