A scalable consistent second-order SPH solver for unsteady low Reynolds number flows
A scalable consistent second-order SPH solver for unsteady low Reynolds number flows
复制标题
用于不稳定低雷诺数流的可扩展一致二阶 SPH 求解器
DOI：
10.1016/j.cma.2014.12.027
复制
发表时间：
2015
影响因子：
7.2
通讯作者：
Jinchao Xu
中科院分区：
文献类型：
--
作者：
Nathaniel Trask;M. Maxey;Kyungjoo Kim;M. Perego;M. Parks;Kai Yang;Jinchao Xu
光滑粒子流体动力学（SPH）已成功地用于研究各种情况下，涉及几乎无粘流的守恒性质允许良好的物理近似，尽管差的理论近似性能的微分算子。当用于研究非定常低雷诺数大耗散流动时，仅仅守恒不能保证近似质量，传统的方法是不一致的。另一种提法最近变得流行，利用近似分裂计划，以确保无发散的速度场。然而，该方案依赖于拉普拉斯算子的不一致离散化，该离散化随着颗粒在流动下变得无序而发散。我们提出了一个增量压力校正方案和现有的微分算子重整化的组合，能够实现二阶精度的时间和空间。简要回顾了SPH近似理论，强调了这些重正化在实现近似因式分解方案中的必要性。我们证明，当快速代数多重网格预处理器用于解决所产生的线性系统，该计划的结果是一致的近似，是可扩展的，适合并行化。几个验证的情况下，实现了几个数量级的加速比传统的SPH方法。最后，已经开发了一个接口之间的粒子库LAMMPS和稀疏线性代数库Trilinos提供了一个大规模并行的三维SPH能力。沿着展示了32，768个岩心上多达1.34亿个颗粒的缩放结果，并演示了模拟复杂3D几何形状的能力。这些结果表明，应用必要的一致性校正的增加的复杂性实际上提供了四倍的加速每个线性求解器迭代与未校正的情况下，尽管构建校正的额外成本。由此产生的库提供了一种方法，是一致的，高效的，在空间和时间上的二阶，同时保持经典的SPH单相流的灵活性。
Smoothed Particle Hydrodynamics (SPH) has successfully been used to study a variety of cases involving nearly inviscid flows where conservation properties allow for good physical approximation despite poor theoretical approximation properties of differential operators. When used to study unsteady low Reynolds number flow with large dissipation, conservation alone cannot ensure quality of approximation and the traditional approach is inconsistent. An alternative formulation has recently become popular making use of an approximate splitting scheme to ensure a divergence-free velocity field. However, this scheme relies on an inconsistent discretization of the Laplacian that diverges as particles become disordered under flow. We present an incremental pressure correction scheme and combination of existing differential operator renormalizations that are able to achieve second order accuracy in time and space. A brief review of SPH approximation theory is provided to highlight the necessity of these renormalizations in implementing an approximate factorization scheme. We demonstrate that when fast algebraic multigrid preconditioners are used to solve the resulting linear systems, the scheme results in a consistent approximation that is scalable and amenable to parallelization. Several validation cases are presented for which a speedup of several orders of magnitude is achieved over traditional SPH approaches. Finally, an interface has been developed between the particle library LAMMPS and the sparse linear algebra libraries in Trilinos providing a massively parallel 3D SPH capability. Scaling results for up to 134 million particles on 32,768 cores are presented along with a demonstration of the capability to simulate complex 3D geometries. These results show that the added complexity of applying the necessary consistency corrections actually provides a factor of four speed-up per linear solver iteration versus the uncorrected case, despite the additional cost of constructing the corrections. The resulting library provides a method that is consistent, efficient, and second order in both space and time while maintaining the flexibility of classical SPH for single phase flows.
影响因子：
6.3
作者：
Dominguez, J. M.;Crespo, A. J. C.;Gomez-Gesteira, M.
通讯作者：
Gomez-Gesteira, M.