Some experiments with high order compact methods using a computer algebra software—Part II (non-uniform grid)

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We generalize a procedure proposed by Mancera and Hunt [P.F.A. Mancera, R. Hunt, Some experiments with high order compact methods using a computer algebra software—Part I, Appl. Math. Comput., in press, doi:10.1016/j.amc.2005.05.015] for obtaining a compact fourth-order method to the steady 2D Navier–Stokes equations in the streamfunction formulation—vorticity using the computer algebra system Maple, which includes conformal mappings and non-uniform grids. To analyse the procedure we have solved a constricted stepped channel problem, where a fine grid is placed near the re-entrant corner by transformation of the independent variables.

论文关键词:Fourth-order method,Compact method,Steady 2D Navier–Stokes equations

论文评审过程:Available online 26 January 2006.

论文官网地址:https://doi.org/10.1016/j.amc.2005.11.135