An Efficient Implementation Scheme for the Moving Grid Method Based on Delaunay Graph Mapping

Abstract

Dynamic grid algorithm is essential for numerical simulation of fluid‐structure interaction problems with moving boundaries that require the mesh to be movable or deformable. This paper investigates the computational cost of the dynamic grid deformation method proposed by X. Q. Liu, N. Qin et al. (see Journal of Computational Physics, 211, 2006, pp.405–423). This method can deal with the large dynamical deformation of a mesh with any given topology based on the Delaunay graph mapping of the original mesh. Facing to the most time consuming parts of the Liu’s approach, a high efficient algorithm and implementation scheme are presented to speed up the method. We have two main improvements. First, a fast locating technique is developed to locate the background element for the mesh points. Second, an efficient scheme is proposed that avoids most of repeated calculations in relocating the mesh points in the graph. Time complexity analysis indicates that the proposed algorithm and implementation scheme has gained substantial speedup compared with the Liu’s original approach, while the memory requirement is even decreased. Several testing examples are given to demonstrate the efficiency of the proposed approach.