A fourth-order-accurate difference approximation for the incompressible Navier-Stokes equations

We discuss fourth-order-accurate difference approximations for parabolic systems and for the incompressible Navier-Stokes equations. A general principle for deriving numerical boundary conditions for higher-order-accurate difference schemes is described. Some difference approximations for parabolic systems are analyzed for stability and accuracy. The principle is used to derive stable and accurate numerical boundary conditions for the incompressible Navier-Stokes equations. Numerical results are given from a fourth-order-accurate scheme for the incompressible Navier-Stokes equations on overlapping grids in two- and three-space dimensions. © 1994.