物理质团法:一个普适的数值方法体系

计算物理 ›› 2017, Vol. 34 ›› Issue (3): 261-272.

物理质团法:一个普适的数值方法体系

马智博

北京应用物理与计算数学研究所, 北京 100094

收稿日期:2016-04-12 修回日期:2016-06-18 出版日期:2017-05-25 发布日期:2017-05-25
作者简介:马智博(1963-),男,博士,研究员,主要从事计算物理、可靠性理论与工程研究,E-mail:mazhibo@iapcm.ac.cn

Physics Evoked Cloud Method: A Versatile Systematic Method for Numerical Simulations

MA Zhibo

Institute of Applied Physics and Computational Mathematics, Beijing 100094, China

Received:2016-04-12 Revised:2016-06-18 Online:2017-05-25 Published:2017-05-25

摘要/Abstract

摘要： 无网格方法根据分布于近邻空间各个方向的微元体物理信息构造离散方程，显著降低了空间导数计算对微元体本身及微元体之间拓扑结构的条件限制，极大提高了拉氏方法的大变形计算能力.由于不能利用微元体的完备几何信息，不容易构造符合物理的无网格算法，对那些物理参数存在间断的模型对象，难以获得稳定和准确的计算结果.本文基于对物理规律及数值模拟发展趋势的分析，提出符合物理且具有强普适性的无网格方法体系.基于该方法的一维算例表明，即使物理参数存在强烈间断，数值结果也能很好地逼近问题的真解.

关键词: 数值模拟, 无网格方法, 光滑粒子法, 物理质团法

Abstract: In mesh free methods, discrete equations are built according to physics information of micro-bodies arbitrarily spread in vicinal space. As requirements about topology of micro-bodies are reduced, simulations with Lagrangian approach may be easier even with large distortions. Owing to insufficiency of topological information, there is a challenge for mesh-free method to reflect physics especially as discontinuities exist. In this paper a new mesh free systematic method PECM (Physics Evoked Cloud Method) based on physical laws and developing trend of numerical simulation is shown, which has excellent applicability. High fidelity to physics of the method is demonstrated through several 1-dimentional problems in which strong discontinuities exist.

Key words: numerical simulation, mesh free method, SPH, PECM

中图分类号:

O242.1

马智博. 物理质团法:一个普适的数值方法体系[J]. 计算物理, 2017, 34(3): 261-272.

MA Zhibo. Physics Evoked Cloud Method: A Versatile Systematic Method for Numerical Simulations[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2017, 34(3): 261-272.

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