High order compact computation and nonuniform grids for streamfunction vorticity equations

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Fourth order compact difference schemes for steady streamfunction vorticity formulation of 2D incompressible Navier–Stokes equations on nonuniform grids are derived using Maple software package. Especially we deduce fourth order compact difference scheme of the first partial derivative terms. In order to resolve boundary layers, grid transformation techniques are used, which maps a nonuniform grid onto a uniform one for use with the fourth order compact difference scheme. A Krylov subspace iterative method with an ILUT preconditioning technique is employed to solve the resulting linear system. The proposed high accuracy computation method is applied to two model problems. Computational results are compared with results computed by other schemes in the literature.