定常不可压Navier-Stokes方程的并行有限元算法  

Parallel finite element algorithms for the steady incompressible Navier-Stokes equations

作　　者：尚月强 郑波 周康瑞 丁琪 SHANG Yueqiang;ZHENG Bo;ZHOU Kangrui;DING Qi(School of Mathematics and Statistics,Southwest University,Chongqing 400715,China)

机构地区：[1]西南大学数学与统计学院,重庆北碚400715

出　　处：《贵州师范大学学报（自然科学版）》2020年第3期1-12,F0003,共13页Journal of Guizhou Normal University：Natural Sciences

基　　金：国家自然科学基金(11361016);重庆市基础与前沿探索研究计划(cstc2018jcyjAX0305);中央高校基本科研业务费专项(XDJK2018B032);重庆市研究生科研创新项目(CYS19085)资助。

摘　　要：Navier-Stokes(N-S)方程组是描述流体运动的基本方程组,其数值模拟对我国的国防建设与工业设计非常重要。在高性能并行机和并行计算技术飞速发展的今天,其并行数值计算方法的研究是当前计算流体力学领域最前沿的热门课题之一。基于局部与并行有限元离散技巧和区域分解方法,给出了数值求解定常不可压N-S方程的若干高效并行算法,这些算法实现简单,稍加修改现有的串行程序即可实现并行计算,通信需求少,能快速有效地模拟复杂的流体流动行为。我们给出了一些理论结果和数值算例,验证这些算法的有效性。Navier-Stokes equations are the basic mathematical model describing the motion of a fluid,and their numerical simulation plays a very important role in the development of national defense and industrial design.With the rapid development of high-performance parallel computers and parallel computing technology,the development of parallel numerical methods for the Navier-Stokes equations is one of the most popular research topics in the field of computational fluid dynamics.This paper gives some efficient parallel algorithms for numerically solving the steady incompressible Navier-Stokes equations based local and parallel finite element discretizations and domain decomposition method.These algorithms are easy to implement based on a sequential solver without extensive recoding,have low communication costs,and can efficiently simulate the complicated behaviors of flows.We also give some theoretical results and numerical results to demonstrate the effectiveness of the algorithms.

关 键 词：NAVIER-STOKES方程 有限元方法 并行算法 区域分解方法 两重网格方法 

分 类 号：O241.8[理学—计算数学]