On multigrid methods for the solution of least-squares finite element models for viscous flows

作     者：Ranjan, Rakesh Reddy, J. N. 

作者机构：Univ Texas San Antonio Dept Mech Engn San Antonio TX USA Texas A&M Univ Dept Mech Engn College Stn TX 77843 USA 

出 版 物：《INTERNATIONAL JOURNAL OF COMPUTATIONAL FLUID DYNAMICS》 (国际计算流体动力学杂志)

年 卷 期：2012年第26卷第1期

页      面：45-65页

核心收录：

学科分类：080704[工学-流体机械及工程] 080103[工学-流体力学] 08[工学] 0807[工学-动力工程及工程热物理] 0702[理学-物理学] 0801[工学-力学（可授工学、理学学位）] 

基　　金：Texas A & M University supercomputing centre 

主　　题：multigrid least-squares driven cavity least-squares finite element method backward facing step parallel multigrid 

摘      要：There is a vast literature on least-squares finite element models (LSFEM) applied to fluid dynamics problems. The hp version of the least-squares models is computationally expensive, which necessitates the usage of elegant methods for solving resulting systems of equations. Amongst some of the schemes used for solving large systems of equations is the element-by-element (EBE) solution technique, which has found widespread use in least-squares applications. However, the use of EBE techniques with Jacobi preconditioning leads to very little performance gains as compared to solving a non-preconditioned system. Because of such considerations, the hp version LSFEM solutions are computationally intensive. In this study, we propose to solve the LSFEM systems using the multigrid method, which offers superior convergence rates compared to the EBE-JCG. We demonstrate the superior convergence of the Multigrid solver compared to Jacobi preconditioning for the wall-driven cavity and backward facing step problems using the full Navier-Stokes equations. Load balancing issues encountered with multigrid solvers in a parallel environment are resolved elegantly with an element-by-element solution of the coarse grid problem with Jacobi preconditioning.