Grid and metric generation on the assembly of locally bi-quadratic coordinate transformations

The generation of metric coefficients of the coordinate transformation from a generally curved-sided domain boundary to the unit square (cube) is required for efficient solution algorithms in computational fluid mechanics. An algebraic procedure is presented for establishment of these data on the union of arbitrarily selected sub-domains of the global solution domain. A uniformly smooth progression of grid refinement is readily generated, including multiple specification of refined grids for a given macro-element domain discretization. The procedure is illustrated as generally applicable to non-simply connected domains in two and three dimensions.