High-order compact scheme for the steady stream-function vorticity equations. (English) Zbl 0836.76065

Summary: A higher-order compact scheme that is \(O(h^4)\) on the nine-point two- dimensional stencil is formulated for the steady stream-function vorticity form of the Navier-Stokes equations. The resulting stencil expressions are presented and hence this new scheme can be easily incorporated into existing industrial software. We also show that special treatment of the wall boundary conditions is required. The method is tested on representative model problems and compares very favourably with other schemes in the literature.


76M20 Finite difference methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
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