A Moving Point Method for Arbitrary Peclet Number Multi-Dimensional Convection—Diffusion Equations

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Abstract
The moving point algorithm of Garder, Peaceman & Pozzi (SPEJ, March 1964, 26–36) will solve high Peclet number, multi-dimensional, convection-diffusion equations without numerical diffusion or spurious oscillations. The method uses a moving set of points together with a fixed Eulerian mesh and avoids the mesh tangling problems of many moving mesh methods. However, numerical results of Price, Cavendish & Varga (SPEJ, Sept. 1968, 293–303) indicate that with a fixed number of moving points per mesh cell the algorithm does not converge under mesh refinement. These authors also show, for fixed mesh lengths and a fixed number of moving points per cell, that the moving point method is more accurate than conventional fixed-mesh algorithms if the Peclet number is sufficiently large. We introduce and analysis a moving point algorithm which we prove to converge for arbitrary Peclet numbers. Numerical results demonstrating the convergence and the accuracy of the moving point method relative to standard finite difference algorithms are described.

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