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A compact fourth-order finite difference scheme for the steady incompressible Navier-Stokes equations. (English) Zbl 0836.76060
Summary: We note that the Navier-Stokes equations, when expressed in streamfunction-vorticity form, can be approximated to fourth-order accuracy with stencils extending only over a 3×3 square of points. The key advantage of the new compact fourth-order scheme is that it allows direct iteration for low-to-moderate Reynolds numbers. Numerical solutions are obtained for the model problem of the driven cavity and compared with solutions available in the literature. For Re7500 point-SOR iteration is used, and the convergence is fast.

MSC:
76M20Finite difference methods (fluid mechanics)
76D05Navier-Stokes equations (fluid dynamics)