Study on Truncation Error in General Coordinate System and Optimized Grid Generation for Natural Rivers

Abstract

Grid structures of the general curvilinear coordinate system with gross distortions have never given solutions of the hydraulic equation even under accurately computations. A relationship between a quality of the grid structure and a stability of computations has not quantitatively investigated. This study shows that a estimation method for truncation error of metrics of the grid structure and the method can detect instability of solution without numerical computation. An optimization method for the grid structures with the elliptic partial differential equation can effectively reduce the truncation error and derive physical solution.