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 Hodge 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.
Kupferman
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Mathematics Department, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, 50A-2152, Berkeley, CA 94720, USA.
Tadmor
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