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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 161873, 13 pages
Research Article

A Pressure-Stabilized Lagrange-Galerkin Method in a Parallel Domain Decomposition System

School of Engineering, Sun Yat-Sen University, 510275 Guangzhou, China

Received 30 April 2013; Accepted 14 June 2013

Academic Editor: Santanu Saha Ray

Copyright © 2013 Qinghe Yao and Qingyong Zhu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A pressure-stabilized Lagrange-Galerkin method is implemented in a parallel domain decomposition system in this work, and the new stabilization strategy is proved to be effective for large Reynolds number and Rayleigh number simulations. The symmetry of the stiffness matrix enables the interface problems of the linear system to be solved by the preconditioned conjugate method, and an incomplete balanced domain preconditioner is applied to the flow-thermal coupled problems. The methodology shows good parallel efficiency and high numerical scalability, and the new solver is validated by comparing with exact solutions and available benchmark results. It occupies less memory than classical product-type solvers; furthermore, it is capable of solving problems of over 30 million degrees of freedom within one day on a PC cluster of 80 cores.