A HIGH-RESOLUTION FINITE-DIFFERENCE SCHEME FOR NONUNIFORM GRIDS

A higher-order, high-resolution finite-difference scheme for nonuniform grids is presented. This scheme, derived rigorously form Taylor series expansion at nomuniform gridpoints with a total-variation-diminishing constraint applied, gives better numerical approximations to the analytical solutions compared with schemes that are only first-order when applied to nonuniform grids. The scheme is suitable even for extremely nonuniform grids, which are often required in large-scale simulation problems. A wide range of flexibility in designing nonuniform grids is achieved.