SPH二阶粒子近似光滑函数的充分条件及数值验证

doi:10.19596/j.cnki.1001-246x.7807

计算物理 ›› 2019, Vol. 36 ›› Issue (1): 25-38.DOI: 10.19596/j.cnki.1001-246x.7807

SPH二阶粒子近似光滑函数的充分条件及数值验证

徐丞君¹, 徐胜利²

1. 中国科学技术大学数学学院, 合肥 230026;
2. 清华大学航天航空学院, 北京 100084

收稿日期:2017-12-06 修回日期:2018-02-09 出版日期:2019-01-25 发布日期:2019-01-25
通讯作者: 徐胜利,E-mail:slxu@mail.tsinghua.edu.cn
作者简介:徐丞君(1991-),男,硕士研究生,研究方向为界面流动数值模拟,E-mail:xucjh@mail.ustc.edu.cn
基金资助:
国家自然科学基金（11471305）及中国运载火箭技术研究院基金（CALT201601）及清华大学自主课题（20161080102）资助项目

Sufficient Conditions and Numerical Validations for Smooth Functions in Particle Approximation of SPH Scheme

XU Chengjun¹, XU Shengli²

1. School of Mathematics, University of Science and Technology of China, Hefei 230026, China;
2. School of Aerospace Engineering, Tsinghua University, Beijing 100084, China

Received:2017-12-06 Revised:2018-02-09 Online:2019-01-25 Published:2019-01-25

摘要/Abstract

摘要： 为实现SPH二阶粒子近似，讨论光滑函数应满足的充分条件，给出对应的光滑函数形式，分析二阶粒子近似解的唯一性，并进行数值验证.结果表明：和标准SPH方法相比，在周期边界条件下，随着粒子数加密，SPH方法二阶粒子近似的L₁误差减小且L₁阶趋近2.0.

关键词: SPH方法, 光滑函数, 粒子近似, 数值模拟

Abstract: To obtain second order accuracy in SPH scheme, sufficient conditions for smooth functions are discussed and formula are presented. Uniqueness is analyzed for solution of the second order particle approximation. SPH approximate solutions are numerically validated to arrive at nearly second accuracy in the case of periodic boundary conditions. While particle number increases, L₁-error decreases and L₁-order approaches to the second order particle approximation of SPH scheme.

Key words: SPH scheme, smooth function, particle approximation numerical simulation

中图分类号:

O241.5

徐丞君, 徐胜利. SPH二阶粒子近似光滑函数的充分条件及数值验证[J]. 计算物理, 2019, 36(1): 25-38.

XU Chengjun, XU Shengli. Sufficient Conditions and Numerical Validations for Smooth Functions in Particle Approximation of SPH Scheme[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2019, 36(1): 25-38.

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SPH二阶粒子近似光滑函数的充分条件及数值验证

Sufficient Conditions and Numerical Validations for Smooth Functions in Particle Approximation of SPH Scheme

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