一维理想弹塑性流体的数值模拟及壁热现象的抑制

doi:10.19596/j.cnki.1001-246x.8141

计算物理 ›› 2020, Vol. 37 ›› Issue (5): 539-550.DOI: 10.19596/j.cnki.1001-246x.8141

所属专题：第十届全国青年计算物理会议优秀论文

一维理想弹塑性流体的数值模拟及壁热现象的抑制

李肖^1,2, 孙晨¹, 沈智军¹

1. 北京应用物理与计算数学研究所, 北京 100088;
2. 中国工程物理研究院研究生院, 北京 100088

收稿日期:2019-09-17 修回日期:2020-01-08 出版日期:2020-09-25 发布日期:2020-09-25
通讯作者: 沈智军(1966-),男,研究员,主要从事流体力学计算方法研究,E-mail:shen_zhijun@iapcm.ac.cn
作者简介:李肖(1991-),男,博士研究生,主要从事流体力学计算方法研究,E-mail:lixiaosci0720@163.com
基金资助:
科学挑战专题（JCKY2016212A502）、国家自然科学基金（U1630249，11971071）和计算物理实验室基金资助项目

Numerical Simulation of One-dimensional Elastic-Perfectly Plastic Flow and Suppression of Wall Heating Phenomenon

LI Xiao^1,2, SUN Chen¹, SHEN Zhijun¹

1. Institute of Applied Physics and Computational Mathematics, Beijing 100088, China;
2. Graduate School of China Academy of Engineering Physics, Beijing 100088, China

Received:2019-09-17 Revised:2020-01-08 Online:2020-09-25 Published:2020-09-25

摘要/Abstract

摘要： 针对一维理想弹塑性流体的Wilkins模型，提出HLLC型的近似黎曼解法器.该解法器引入塑性波并保证波的个数和真实的物理情况一致，其中波速选取由波系的特征分析来确定.整个算法实施简单，无需迭代，为减少强冲击（稀疏）模拟时的壁热误差，设计相应的壁热粘性，有效地抑制了非物理的壁热现象.

关键词: 弹塑性流体, 塑性波, 黎曼解法器, HLLC, 壁热现象

Abstract: An HLLC-type approximate Riemann solver is proposed to simulate one-dimensional elastic-perfectly plastic flow with Wilkins model. This Riemann solver introduces plastic wave and has the same wave number with actual physics. The wave speed is determined by characteristic analysis of wave system. The algorithm is simple to implement and does not need iteration. In order to reduce wall heating error in the simulation for strong shock (or rarefaction), wall heating viscosity is designed to effectively suppress the non-physical wall heating phenomenon.

Key words: elastic-plastic flow, plastic wave, Riemann solver, HLLC, wall heating phenomenon

中图分类号:

O354

李肖, 孙晨, 沈智军. 一维理想弹塑性流体的数值模拟及壁热现象的抑制[J]. 计算物理, 2020, 37(5): 539-550.

LI Xiao, SUN Chen, SHEN Zhijun. Numerical Simulation of One-dimensional Elastic-Perfectly Plastic Flow and Suppression of Wall Heating Phenomenon[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2020, 37(5): 539-550.

参考文献

[1] WILKINS M L. Calculation of elastic-plastic flow[J]. Journal of Biological Chemistry, 1964, 280(13):12833-12839.
[2] TRANGENSTEIN J A, COLELLA P. A higher-order Godunov method for modeling finite deformation in elastic-plastic solids[J]. Communications on Pure & Applied Mathematics, 2010, 44(1):41-100.
[3] MILLER G H, COLELLA P. A high-order Eulerian Godunov method for elastic-plastic flow in solids[J]. Journal of Computational Physics, 2001, 167(1):131-176.
[4] BURTON D E, CARNEY T C, MORGAN N R, et al. A cell-centered Lagrangian Godunov-like method for solid dynamics[J]. Computers & Fluids, 2013, 83:33-47.
[5] KLUTH G, DESPRES B. Discretization of hyperelasticity on unstructured mesh with a cell-centered Lagrangian scheme[J]. Journal of Computational Physics, 2010, 229(24):9092-9118.
[6] MAIRE P H, ABGRALL R, BREIL J, et al. A nominally second-order cell-centered Lagrangian scheme for simulating elastic-plastic flows on two-dimensional unstructured grids[J]. Journal of Computational Physics, 2013, 235(Complete):626-665.
[7] GAO S, LIU T G. 1D exact elastic-perfectly plastic solid Riemann solver and its multi-material application[J]. Advances in Applied Mathematics and Mechanics, 2017, 9(03):621-650.
[8] CHENG J B, TORO E F, JIANG S, et al. A high-order cellcentered Lagrangian scheme for one-dimensional elastic-plastic problems[J]. Computers & Fluids, 2015, 122:136-152.
[9] CHENG J B. Harten-Lax-van Leer-contact (HLLC) approximation Riemann solver with elastic waves for one-dimensional elastic-plastic problems[J]. Applied Mathematics and Mechanics, 2016, 37(11):1517-1538.
[10] LIU L, CHENG J B. A multi-material HLLC Riemann solver with both elastic and plastic waves for 1D elastic-plastic flows[J]. Computers and Fluids, 2019, 192:104265.
[11] WANG R L, LIN Z, WEN L, et al. Wall heating and Q&H method in arbitrary n-polygon Lagrange grids finite volume method[J]. Chinese Journal of Computational Physics, 2007, 24(4):407-412.
[12] SHEN Z J, XIE Y W, YAN W. Wall heating and adaptive heat conduction viscosity[J]. Chinese Journal of Computational Physics, 2012, 29(6):807-814.
[13] SHEN Z J, LV G X, SHEN L J. Riemann solver and artificial viscosity in SPH[J]. Mathematica Numerica Sinica, 2006, 28(4):433-448.
[14] VONNEUMANN J, RICHTMYER R D. A method for the numerical calculation of hydrodynamic shocks[J]. Journal of Applied Physics, 1950, 21(3):232-237.

一维理想弹塑性流体的数值模拟及壁热现象的抑制

Numerical Simulation of One-dimensional Elastic-Perfectly Plastic Flow and Suppression of Wall Heating Phenomenon

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