基于二重网格的动网格松弛法改进

An improvement on the dynamic mesh method of sphere relaxation using double grids

相比传统的弹簧法等方法,基于球松弛算法的动网格松弛法在复杂边界大变形条件下可以得到质量更高的边界网格以及更大的极限变形量,但该方法在时间效率上还有提升的空间。引入二重网格,采用动网格松弛法进行稀疏网格的网格变形,将边界位移传递到整个网格计算域;再利用二重网格映射,将稀疏网格位移映射到原有计算网格的节点上。算例表明,改进后的动网格松弛法在极限变形量和变形后网格质量基本保持不变的情况下,能够有效地提高网格变形的计算效率。此外还研究了二重网格的粗细网格节点数之比(粗网格为稀疏网格,细网格为原计算网格)对网格变形的影响,算例表明最佳计算效率出现在粗细网格节点数之比为0.5左右时。

The dynamic mesh method based on the sphere relaxation algorithm generates boundary meshes with higher quality and achieves larger deformation than the traditional spring method even for large boundary deformations.However,the time efficiency of this method still has room for improvement.In this work,we present a double-grid strategy which introduces a coarse mesh besides the computational mesh(fine mesh).The sphere relaxation algorithm is applied to deform the coarse mesh and transfer the boundary displacement to the entire region.Then,the double-grid mapping is carried out to map the displacements of the coarse mesh into the computational mesh.Numerical examples show that the improved method effectively increases the mesh deformation efficiency while the deformation ability and mesh quality remain.We also study the effects of the node number ratio(coarse mesh/fine mesh)on the mesh deformation.Numerical examples indicate that the optimal node number ratio is about 0.5 for the highest efficiency.