A compact fourth‐order finite difference scheme for the steady incompressible Navier‐Stokes equations

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Abstract
We note in this study 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 x 3 square of points. The key advantage of the new compact fourth‐order scheme is that it allows direct iteration for low‐to‐medium Reynolds numbers. Numerical solutions are obtained for the model problem of the driven cavity and compared with solutions available in the literature. For Re ⩽ 7500 point‐SOR iteration is used and the convergence is fast.