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首页> 外文期刊>Journal of Computational Physics >Parallel finite element simulations of incompressible viscous fluid flow by domain decomposition with Lagrange multipliers
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Parallel finite element simulations of incompressible viscous fluid flow by domain decomposition with Lagrange multipliers

机译：拉格朗日乘子域分解对不可压缩粘性流体流动的并行有限元模拟

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摘要

A parallel approach to solve three-dimensional viscous incompressible fluid flow problems using discontinuous pressure finite elements and a Lagrange multiplier technique is presented. The strategy is based on non-overlapping domain decomposition methods, and Lagrange multipliers are used to enforce continuity at the boundaries between subdomains. The novelty of the work is the coupled approach for solving the velocity-pressure-Lagrange multiplier algebraic system of the discrete Navier-Stokes equations by a distributed memory parallel ILU (0) preconditioned Krylov method. A penalty function on the interface constraints equations is introduced to avoid the failure of the ILU factorization algorithm. To ensure portability of the code, a message based memory distributed model with MPI is employed. The method has been tested over different benchmark cases such as the lid-driven cavity and pipe flow with unstructured tetrahedral grids. It is found that the partition algorithm and the order of the physical variables are central to parallelization performance. A speed-up in the range of 5-13 is obtained with 16 processors. Finally, the algorithm is tested over an industrial case using up to 128 processors. In considering the literature, the obtained speed-ups on distributed and shared memory computers are found very competitive.
机译：提出了一种使用不连续压力有限元和拉格朗日乘数技术解决三维粘性不可压缩流体流动问题的并行方法。该策略基于非重叠域分解方法，拉格朗日乘数用于强制子域之间边界的连续性。这项工作的新颖之处在于采用分布式存储并行ILU（0）预处理Krylov方法求解离散Navier-Stokes方程的速度-压力-拉格朗日乘数代数系统的耦合方法。为了避免ILU分解算法的失败，引入了对接口约束方程的惩罚函数。为了确保代码的可移植性，采用了带有MPI的基于消息的内存分布式模型。该方法已在不同的基准情况下进行了测试，例如盖驱动的空腔和具有非结构化四面体网格的管道流动。发现分区算法和物理变量的顺序对于并行化性能至关重要。使用16个处理器可获得5-13的加速范围。最后，该算法在工业案例中使用多达128个处理器进行了测试。在考虑文献时，发现在分布式和共享存储计算机上获得的加速非常有竞争力。

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