A Pressure-Stabilized Lagrange-Galerkin Method in a Parallel Domain Decomposition System
A Pressure-Stabilized Lagrange-Galerkin Method in a Parallel Domain Decomposition System
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DOI：
10.1155/2013/161873
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发表时间：
2013-06
影响因子：
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通讯作者：
Qinghe Yao;Q. Zhu
中科院分区：
文献类型：
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作者：
Qinghe Yao;Q. Zhu
本文在并行域分解系统中实现了压力稳定的拉格朗日-伽辽金方法，并且证明新的稳定策略对于大雷诺数和瑞利数模拟是有效的。刚度矩阵的对称性使得线性系统的界面问题可以通过预条件共轭法求解，并且将不完全平衡域预条件器应用于流热耦合问题。该方法显示出良好的并行效率和高数值可扩展性，并且通过与精确解和可用基准结果进行比较来验证新的求解器。比经典的乘积型求解器占用更少的内存；此外，它还能够在80核的PC集群上一天内解决超过3000万自由度的问题。
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.