An analytical transformation technique for generating uniformly spaced computational mesh

An analytical transformation method which can map arbitrary physical coordinate grid distribution into desired computational coordinate with uniform grid distribution is derived. The transformation function and its higher derivatives are differentiable. Salient features include; (1) precise control of grid sizes; (2) more than one location of clustered grids; (3) exact positioning of particular computational nodes in the physical plane; and (4) ensuring several patches of uniformly spaced grids in the physical plane for the higher accuracies (such as at the boundaries), etc., while keeping the variation of grid spacing continuous to avoid numerical instability.