A fast, high resolution, second-order central scheme for incompressible flows

A high resolution, second-order central difference method for incompressible flows is presented, The method is based on a recent second-order extension of the classic Lax-Friedrichs scheme introduced for hyperbolic conservation laws (Nessyahu H, & Tadmor E, (1990) J. Comp. Physics, 87, 408-463; Jiang G,-S, & Tadmor E, (1996) UCLA CAM Report 96-36, SIAM J, Sci, Comput., in press) and augmented by a new discrete Hedge projection, The projection is exact, yet the discrete Laplacian operator retains a compact stencil, The scheme is fast, easy to implement, and readily generalizable. Its performance was tested on the standard periodic double shear-layer problem; no spurious vorticity patterns appear when the flow is underresolved. A short discussion of numerical boundary conditions is also given, along with a numerical example.