The construction of discrete orthogonal coordinates

Abstract An orthogonalization procedure for the transformation of finite nonorthogonal coordinates to an equivalent finite set of orthogonal coordinates is described. The procedure involves the direct solution of a series of ‘exact’ matrix equations and is independent of the amount of shear or nonorthogonality of the original coordinates. The method may be applied to the solution of complex boundary value problems and generally at each timestep to the Lagrangian solution of multidimensional initial value problems.