High-Order Compact Finite Difference Methods

In this work we present a general approach for developing high-order compact differencing schemes by utilizing the governing differential equation to help approximate truncation error terms. As an illustrative application we consider the stream-function vorticity form of the Navier Stokes equations, and provide driven cavity results. Some extensions to treat non-constant metric coefficients resulting from mapping from a physical to a reference domain and to 3D potential problems are considered. Supporting numerical studies showing the higher-order rates of convergence and the local superconvergence at the nodes are presented.

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