四面体网格上动态负载平衡Euler方程的并行p -自适应间断Galerkin方法

IF 1.7 4区 工程技术 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS
Weizhao Li, Aditya K. Pandare, Hong Luo, Jozsef Bakosi, Jacob Waltz
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引用次数: 0

摘要

提出了一种新的p自适应间断伽辽金(DG)方法来求解三维四面体网格上的欧拉方程。DG空间离散化采用分层正交基函数,时间积分采用三阶TVD龙格-库塔方法。将基于顶点的限制器应用于数值解,以消除高阶方法中的振荡。由阶数解构造的误差指示器,用于调整每个计算元素的自由度,这显著降低了计算成本,同时仍然保持精确的解。所开发的方法是在Charm++并行计算框架下用实现的。Charm++是一个包含各种负载平衡策略的并行计算框架。在Charm++系统下实现数值求解器为我们提供了一套动态负载平衡策略。这可以有效地用于缓解p‐adaptation造成的负载失衡。进行了大量数值实验,以证明所开发的p自适应DG方法的数值精度和并行性能。研究表明,Charm++系统的动态负载平衡可以缓解并行p自适应DG方法造成的负载分布不平衡。因此,可以实现高性能增益。对于当前工作中研究的测试用例,并行性能增益在1.5倍到3.7倍之间。因此,与没有p自适应的标准DG方法相比,所开发的p自适应DG方法可以显著减少总模拟时间。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

A parallel p-adaptive discontinuous Galerkin method for the Euler equations with dynamic load-balancing on tetrahedral grids

A parallel p-adaptive discontinuous Galerkin method for the Euler equations with dynamic load-balancing on tetrahedral grids

A novel p-adaptive discontinuous Galerkin (DG) method has been developed to solve the Euler equations on three-dimensional tetrahedral grids. Hierarchical orthogonal basis functions are adopted for the DG spatial discretization while a third order TVD Runge-Kutta method is used for the time integration. A vertex-based limiter is applied to the numerical solution in order to eliminate oscillations in the high order method. An error indicator constructed from the solution of order ( p ) $$ (p) $$ and ( p 1 ) $$ \left(p-1\right) $$ is used to adapt degrees of freedom in each computational element, which remarkably reduces the computational cost while still maintaining an accurate solution. The developed method is implemented with under the Charm++ parallel computing framework. Charm++ is a parallel computing framework that includes various load-balancing strategies. Implementing the numerical solver under Charm++ system provides us with access to a suite of dynamic load balancing strategies. This can be efficiently used to alleviate the load imbalances created by p-adaptation. A number of numerical experiments are performed to demonstrate both the numerical accuracy and parallel performance of the developed p-adaptive DG method. It is observed that the unbalanced load distribution caused by the parallel p-adaptive DG method can be alleviated by the dynamic load balancing from Charm++ system. Due to this, high performance gain can be achieved. For the testcases studied in the current work, the parallel performance gain ranged from 1.5× to 3.7×. Therefore, the developed p-adaptive DG method can significantly reduce the total simulation time in comparison to the standard DG method without p-adaptation.

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来源期刊
International Journal for Numerical Methods in Fluids
International Journal for Numerical Methods in Fluids 物理-计算机:跨学科应用
CiteScore
3.70
自引率
5.60%
发文量
111
审稿时长
8 months
期刊介绍: The International Journal for Numerical Methods in Fluids publishes refereed papers describing significant developments in computational methods that are applicable to scientific and engineering problems in fluid mechanics, fluid dynamics, micro and bio fluidics, and fluid-structure interaction. Numerical methods for solving ancillary equations, such as transport and advection and diffusion, are also relevant. The Editors encourage contributions in the areas of multi-physics, multi-disciplinary and multi-scale problems involving fluid subsystems, verification and validation, uncertainty quantification, and model reduction. Numerical examples that illustrate the described methods or their accuracy are in general expected. Discussions of papers already in print are also considered. However, papers dealing strictly with applications of existing methods or dealing with areas of research that are not deemed to be cutting edge by the Editors will not be considered for review. The journal publishes full-length papers, which should normally be less than 25 journal pages in length. Two-part papers are discouraged unless considered necessary by the Editors.
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