Parallel Preconditioners for the unsteady Navier-Stokes Equations and applications to Hemodynamics Simulations
Parallel Preconditioners for the unsteady Navier-Stokes Equations and applications to Hemodynamics Simulations
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DOI：
10.1016/j.compfluid.2013.10.034
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发表时间：
2014-03
影响因子：
2.8
通讯作者：
S. Deparis;Gwenol Grandperrin;A. Quarteroni
中科院分区：
文献类型：
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作者：
S. Deparis;Gwenol Grandperrin;A. Quarteroni
我们对大规模并行结构中非定常Navier-Stokes方程的数值解感兴趣。对于四面体非结构化网格和时间推进有限差分格式的线性系统，我们考虑了有效的预调节器，如压力对流扩散（PCD）预调节器、Yosida预调节器、SIMPLE预调节器和代数加性Schwarz预调节器。为了实现并行效率，我们引入了这些预条件的近似版本，基于它们的分解，其中每个因子可以精确地反转或使用一个附加预条件。我们研究了它们在经典基准问题和与血流动力学相关的模拟方面的强大可扩展性，使用多达8192个内核。
We are interested in the numerical solution of the unsteady Navier–Stokes equations on large scale parallel architectures. We consider efficient preconditioners, such as the Pressure Convection-Diffusion (PCD), the Yosida preconditioner, the SIMPLE preconditioner, and the algebraic additive Schwarz preconditioner, for the linear systems arising from finite element discretizations using tetrahedral unstructured meshes and time advancing finite difference schemes. To achieve parallel efficiency, we introduce approximate versions of these preconditioners, based on their factorizations where each factor can be either inverted exactly or using an add-hoc preconditioner. We investigate their strong scalability for both classical benchmark problems and simulations relevant to hemodynamics, using up to 8192 cores.