A fourth-order accurate method for the incompressible navier-stokes equations on overlapping grids

A method is described to solve the time-dependent incompressible Navier-Stokes equations with finite differences on curvilinear overlapping grids in two or three space dimensions. The scheme is fourth-order accurate in space and uses the momentum equations for the velocity coupled to a Poisson equation for the pressure. The boundary condition for the pressure is taken as ∇ · u = 0. Extra numerical boundary conditions 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. Computational results in two and three space dimensions are given. © 1994 Academic Press, Inc.