(From the author’s summary.) A unique formulation to describe the fluid motion is proposed. The present method and the arbitrary Lagrangian- Eulerian (ALE) method have a common feature: they eliminate the cross- streamline numerical diffusion. For this purpose, we suggested a simple grid constraint condition and utilized an accurate discretization procedure. This grid constraint is only applied to the transverse cell face parallel to the local stream velocity, and hence our method for steady state problems naturally reduces to the streamline-curvature method, without solving explicitly the steady streamline-coordinate equations formulated a priori. The approach is found to be robust and stable. It automatically adapts to flow features without resorting to clustering, thereby maintaining rather uniform grid spacing throughout and large time step. Moreover, the method is shown to resolve multi- dimensional discontinuities with a high level of accuracy, similar to that found in one-dimensional problems.