基于L^2-投影及H^1-投影进行不可压缩粘性流体数值模拟的比较:案例分析(英文)  

A Comparison of L^2-projection and H^1-projection Methods for the Numerical Simulation of Incompressible Viscous Fluid Flow: A Case Study

作　　者：王彤[1] 潘从辉[1] Roland Glowinski 

机构地区：[1]休斯顿大学数学系

出　　处：《工程数学学报》2008年第5期761-778,共18页Chinese Journal of Engineering Mathematics

基　　金：NSF Grants (ECS-9527123, CTS-9873236,DMS-9973318, CCR-9902035, DMS-0209066, DMS-0443826)

摘　　要：本文的主要目的是讨论不可压缩粘性流体的Navier-Stokes方程的数值模拟。本文所用的方法是对时间用一阶精度算了分裂离散化,对空间度是用Uzawa方法对L2-投影及H1-投影求解Stokes问题,以及利用类波动方程方法求解平流问题。这两种投影格式都很容易实现。我们利用它们求解经典顶盖驱动方腔流问题直至雷诺数7500都取得了一致结果。当雷诺数处于区间[8575,8590](对应[8600,8625])时,运用L2-投影(对应H1-投影)得到的结果具有时间周期性,这表明Hopf分支的产生。当雷诺数为10000时,存在两个主导频率相互作用。The main goal of this article is to discuss the numerical solution of the Navier-Stokes equations modeling incompressible viscous fluid flow via methodology combining time dis-cretization by a first order accurate operator-splitting, L2-projection and H1-projection Stokes solvers a la Uzawa and a wave-like equation treatment of the advection. The nu-merical results obtained for the classical wall-driven cavity flow problem show that both methodologies, which are fairly simple to implement, yield consistent results for Reynolds numbers （Re） up to 7500. When Re is in [8575, 8590] （resp., [8600, 8625]） the flow ob-tained by the L2-projection （resp., H1-projection） becomes periodic in time indicating the occurrence of a Hopf bifurcation. The numerical results for Re = 10000 show that two dominant frequencies interact.

关 键 词：NAVIER-STOKES方程 有限元方法 L2-投影及H1-投影方法 类波动方程方法 顶盖驱动方腔流 

分 类 号：O241.82[理学—计算数学]