A compact gas-kinetic scheme with scalable hp multigrid acceleration for steady-state computation on 3D unstructured meshes

IF 3.4 2区物理与天体物理 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Computer Physics Communications Pub Date : 2025-09-11 DOI:10.1016/j.cpc.2025.109820

Hongyu Liu , Xing Ji , Yunpeng Mao , Yuan Ding , Kun Xu

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引用次数: 0

Abstract

In this paper, we present an advanced high-order compact gas-kinetic scheme (CGKS) for 3D unstructured mixed-element meshes, augmented with a hp multigrid technique to accelerate steady-state convergence. The scheme evolves cell-averaged flow variables and their gradients on the original mesh. Mesh coarsening employs a two-step parallel agglomeration algorithm, utilizing a random hash for cell interface selection and a geometric skewness metric for deletion confirmation, thereby ensuring both efficiency and robustness. For the coarser meshes, first-order kinetic flux vector splitting (KFVS) schemes with explicit or implicit time-stepping are used. The proposed multigrid CGKS is tested across various flow regimes on hybrid unstructured meshes, demonstrating significant improvements. A three-level V-cycle multigrid strategy, coupled with an explicit forward Euler method on coarser levels, results in a convergence rate up to ten times faster than standard CGKS. In contrast, the implicit lower-upper symmetric Gauss-Seidel (LU-SGS) method offers limited convergence acceleration. Scalability tests have demonstrated that GMG-CGKS exhibits consistent performance across varying numbers of CPU cores, highlighting its outstanding scalability. Our findings indicate that the explicit multigrid CGKS is highly scalable and effective for large-scale computations, marking a substantial step forward in computational fluid dynamics.

Program summary

Program title: GMG-CGKS-v0.1

CPC Library link to program files: https://doi.org/10.17632/t97mh5c78g.1

Developer's repository link: https://github.com/kevinhongyu/GMG-CGKS-v0.1.git

Programming language: C++

Licensing provisions: GPLv2

External Libraries: METIS, MPI, HDF5

Nature of problem: The program is designed to solve the compressible Euler and Navier-Stokes equations, which are widely used in aerodynamics. The program provides steady-state acceleration techniques for third-order CGKS.

Solution method: A three-level geometric multigrid scheme is adopted to improve the convergence rate of CGKS.

查看原文本刊更多论文

一种具有可扩展hp多网格加速的紧凑气体动力学方案，用于三维非结构化网格的稳态计算

在本文中，我们提出了一种先进的高阶紧凑气体动力学格式（CGKS），用于三维非结构化混合单元网格，并辅以hp多重网格技术来加速稳态收敛。该方案在原始网格上演化单元平均流变量及其梯度。网格粗化采用两步并行集聚算法，利用随机哈希选择单元界面，利用几何偏度度量进行删除确认，从而保证了效率和鲁棒性。对于粗糙网格，采用显式或隐式时间步进的一阶动力学通量矢量分裂（KFVS）格式。提出的多网格CGKS在混合非结构化网格上进行了不同流态的测试，显示出显著的改进。一种三级v循环多网格策略，结合在较粗的层次上的显式正演欧拉方法，其收敛速度比标准CGKS快10倍。相比之下，隐式上下对称高斯-塞德尔（LU-SGS）方法具有有限的收敛加速。可伸缩性测试表明，GMG-CGKS在不同数量的CPU内核上表现出一致的性能，突出了其出色的可伸缩性。我们的研究结果表明，显式多网格CGKS具有高度可扩展性和大规模计算的有效性，标志着计算流体动力学向前迈出了实质性的一步。程序摘要程序标题：GMG-CGKS-v0.1CPC库链接到程序文件：https://doi.org/10.17632/t97mh5c78g.1Developer's存储库链接：https://github.com/kevinhongyu/GMG-CGKS-v0.1.gitProgramming语言：c++许可条款：gplv2外部库：METIS， MPI， hdf5问题性质：该程序旨在解决空气动力学中广泛使用的可压缩欧拉方程和Navier-Stokes方程。该程序为三阶CGKS提供稳态加速技术。求解方法：为了提高CGKS的收敛速度，采用了三层几何多重网格方案。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Computer Physics Communications 物理-计算机：跨学科应用

CiteScore

12.10

自引率

3.20%

发文量

287

审稿时长

5.3 months

期刊介绍： The focus of CPC is on contemporary computational methods and techniques and their implementation, the effectiveness of which will normally be evidenced by the author(s) within the context of a substantive problem in physics. Within this setting CPC publishes two types of paper. Computer Programs in Physics (CPiP) These papers describe significant computer programs to be archived in the CPC Program Library which is held in the Mendeley Data repository. The submitted software must be covered by an approved open source licence. Papers and associated computer programs that address a problem of contemporary interest in physics that cannot be solved by current software are particularly encouraged. Computational Physics Papers (CP) These are research papers in, but are not limited to, the following themes across computational physics and related disciplines. mathematical and numerical methods and algorithms; computational models including those associated with the design, control and analysis of experiments; and algebraic computation. Each will normally include software implementation and performance details. The software implementation should, ideally, be available via GitHub, Zenodo or an institutional repository.In addition, research papers on the impact of advanced computer architecture and special purpose computers on computing in the physical sciences and software topics related to, and of importance in, the physical sciences may be considered.