求解压力Poisson方程的混合粗化代数多重网格算法  

A Algebraic Multigrid Algorithm Based on Hybrid Coarsening for Pressure Poisson Equation

作　　者：胡少亮 许开龙 徐然 刘再刚 徐小文 安恒斌[1,2] 范荣红 汪振宇[3] 王伟 HU Shaoliang;XU Kailong;XU Ran;LIU Zaigang;XU Xiaowen;AN Hengbin;FAN Ronghong;WANG Zhenyu;WANG Wei(Software Center for High Performance Numerical Simulation,China Academy of Engineering Physics,Beijing 100088,China;Institute of Applied Physics and Computational Mathematics,Beijing 100094,China;Institute of Computer Application Technology,China Academy of Engineering Physics,Mianyang,Sichuan 621900,China)

机构地区：[1]中物院高性能数值模拟软件中心,北京100088 [2]北京应用物理与计算数学研究所,北京100094 [3]中国工程物理研究院计算机应用研究所,四川绵阳621900

出　　处：《计算物理》2023年第5期527-534,共8页Chinese Journal of Computational Physics

基　　金：国家自然科学基金(12171045,12102060)资助项目。

摘　　要：针对复杂流动中Navier-Stokes(N-S)方程SIMPLE算法导出的压力Poisson(泊松)离散线性系统,提出一类基于混合粗化的代数多重网格(AMG)算法。该算法采用一类非光滑聚类粗化和经典C/F粗化结合的方式构造网格层次结构,希望在不影响收敛性的情况下,减少AMG算法的启动开销。通过航空发动机燃烧室复杂流动数值模拟应用验证了该算法的有效性。结果表明:对于典型算例,相对于经典AMG算法,该算法可以获得78%的加速。An algebraic multigrid(AMG)algorithm based on hybrid coarsening is proposed for the linear systems of the discrete pressure Poisson which is derived from the SIMPLE algorithm for the Navier-Stokes equations in complex flows.This algorithm combines a class of non-smoothed aggregation coarsening with classical C/F coarsening to construct grid hierarchy,hoping to reduce the cost in the setup phase of the AMG algorithm without affecting convergence.The high performance of the proposed algorithm is verified by numerical simulation of complex flow in the combustion chamber of aero-engine.The results show that the proposed algorithm can achieve 78%acceleration compared with the classical AMG algorithm.

关 键 词：不可压N-S方程 POISSON方程 线性解法器 预条件迭代 代数多重网格 

分 类 号：O246[理学—计算数学]