一种投影浸入边界法的快速直接求解方法

摘要

According to the solving step of proj ected immersed boundary method,after the Poisson equa-tion is discretized,due to the no singularity and the asymmetry of the large sparse linear equation set,the open function library UMFPACK is used for fast solving.When transferring the coefficient matrix and the right end vector,the function library Eigen to optimize the data structure is adapted,which decreases the storage space,finally realize the fast solving and meantime keep the robustness.Firstly,the reliability of solving the pressure Poisson equation is validated by the basic numerical example.Then,according to the numerical method,the corresponding numerical computational program is written by C + +language.The reliability of solving the governing equation of proj ection immersed boundary method is validated by the basic numerical example of flow over circular cylinder compared with results of other lit-eratures.Finally,the distributions of streamline and the vortex structures are analyzed in different Reyn-olds numbers.%根据投影浸入边界法分步投影求解的特点,同时针对压力泊松方程离散后的大型稀疏线性方程组是非奇异非对称的特点,结合开源函数库 UMFPACK,在传递线性方程组的系数矩阵和右端向量时,采用函数库 Eigen将系数矩阵的数据结构改写优化,大大降低了存储空间,实现对高维大型稀疏线性方程组的快速求解,同时求解保持良好的稳定性。本文首先利用一具有解析解的数值算例验证了求解泊松方程数值方法的准确性和网格依赖性,进而利用 VC++编写投影浸入边界法的数值计算程序,以单圆柱绕流为基准数值算例,通过与其他文献和实验结果的对比,验证了投影浸入边界法数值计算结果的可靠性,并进一步分析了不同雷诺数下圆柱绕流的流场结构特征和尾涡结构的动态演化过程。