基于不可压缩流体计算的高效能复预处理算法研究

项目名称： 基于不可压缩流体计算的高效能复预处理算法研究

项目编号： No.11471150

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 数理科学和化学

项目作者： 伍渝江

作者单位： 兰州大学

项目金额： 66万元

中文摘要： 不可压缩流体运动的数值计算，一直是一个充满挑战的研究领域。本项目注意到，目前国际上已将有关近似惯性流形方法、增量未知元方法发展到顶盖驱动方腔流形式的二维不可压缩Navier-Stokes方程的数值计算，其高效能计算问题研究尚处于起步阶段。我们将致力于研究与此问题有关的离散格式及其向复数形式的推广，研究复形式的线性/非线性方程组的高效数值方法，它们的分裂迭代格式设计及理论分析和实际计算，获得有意义的改进。我们还将着重于研究复方程组的新型而高效的偏向一侧的预处理迭代格式，相应的SOR加速技巧。由此进一步探讨适应于复鞍点问题、复广义鞍点问题的改进的修正HSS方法与偏向一侧的高效能预处理算法。

中文关键词： 迭代法；预处理；结构矩阵；鞍点问题；IU方法

英文摘要： Numerical computation for the motion of incompressible fluid flows has been a challenging area of research. This project noted the advances of the approximate inertial manifold method and the incremental unknowns method to the numerical computation of the two-dimensional incompressible Navier-Stokes equations in the form of lid-driven cavity flows. The research of its high efficient computing is still a problem in its infancy. We plan to pay our attention to the study on the discretized schemes related to this issue, and generalize them to forms in complex number. Our study will be on the highly efficient numerical methods for solving complex linear / non-linear equations, on the design of their splitting iterative schemes, theoretical analysis, and actual computation. And we get meaningful improvement afterwards. We will also focus on the study of lopsided preconditioned iterative scheme and its correponding SOR acceleration techniques. Thus adapted to further explore the improved modified HSS methods and the highly efficient lopsided preconditioning algorithms for complex saddle point problems and complex generalized saddle point problems..

英文关键词： itertive method;preconditioning;structured matrix;saddle-point problem;incremental unknowns method