弹塑性问题壁热误差分析及抑制方法

doi:10.19596/j.cnki.1001-246x.8869

计算物理 ›› 2024, Vol. 41 ›› Issue (5): 569-581.DOI: 10.19596/j.cnki.1001-246x.8869

• 第九届全国计算物理会议专栏 • 上一篇下一篇

弹塑性问题壁热误差分析及抑制方法

李肖¹(), 沈智军², 郭虹平²^,³, 方俊², 张红平¹^,*()

1. 深圳技术大学大数据与互联网学院, 广东深圳 518118
2. 北京应用物理与计算数学研究所, 北京 100088
3. 包头师范学院, 数学科学学院, 内蒙古包头 014030

收稿日期:2023-11-28 出版日期:2024-09-25 发布日期:2024-09-14
通讯作者: 张红平
作者简介:李肖, 男, 博士, 主要从事计算流体力学算法研究, E-mail: lixiao_0114@163.com
基金资助:
国家自然科学基金(12302377);国家自然科学基金(11972330);国家自然科学基金(11974321);中国博士后科学基金(2022M722185);广东省基础与应用基础研究基金(2022A1515110521);内蒙古自治区高等学校科学技术研究项目(NJZY19186)

Analyse and Suppression Method of Wall Heating Error for Elastic-Plastic Problem

Xiao LI¹(), Zhijun SHEN², Hongping GUO²^,³, Jun FANG², Hongping ZHANG¹^,*()

1. College of Big Data and Internet, Shenzhen Technology University, Shenzhen, Guangdong 518118, China
2. Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
3. Faculty of Mathematics, Baotou Teachers' College, Baotou, Inner Mongolia 014030, China

Received:2023-11-28 Online:2024-09-25 Published:2024-09-14
Contact: Hongping ZHANG

摘要/Abstract

摘要：

使用单元中心型拉氏Godunov方法, 研究理想弹塑性流体的数值格式和减少壁热误差的方法。给出Godunov格式的黏性修正方程, 描述初值间断情况下黏性激波的形成和传播过程, 分析修正方程的黏性行为和壁热误差的关系。在此基础上, 提出一个HLLC型近似黎曼解法器。在该解法器中, 引入一种自适应热通量黏性项用来抑制界面处的内能和密度壁热误差; 提出一个额外接触速度用来抑制偏应力的过热现象。

关键词: 弹塑性流体, 黎曼解法器, HLLC, 壁热

Abstract:

This paper studies numerical scheme and suppression method of wall heating error for elastic-plastic flow with cell-centered Lagrange Godunov method. Provide the viscosity correction equation of Godunov scheme, describe the procedure of a viscous shock formation and propagation with a jump type initial data, and analyze the relationship between the viscosity behavior of the correction equation and wall heating error. On this basis, a new HLLC-type approximate Riemann solver is proposed. In this solver, an adaptive heat conduction viscosity is introduced to suppress wall heating error of internal energy and density at the interface; What's more, an additional contact velocity is proposed to suppress the over-heating phenomenon of deviatoric stress.

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

中图分类号:

李肖, 沈智军, 郭虹平, 方俊, 张红平. 弹塑性问题壁热误差分析及抑制方法[J]. 计算物理, 2024, 41(5): 569-581.

Xiao LI, Zhijun SHEN, Hongping GUO, Jun FANG, Hongping ZHANG. Analyse and Suppression Method of Wall Heating Error for Elastic-Plastic Problem[J]. Chinese Journal of Computational Physics, 2024, 41(5): 569-581.

图/表 11

图1 网格剖分

Fig.1 Mesh division

图2 HLLCE解法器波结构

Fig.2 Wave structure of HLLCE solver

图3 HLLE解法器波结构

Fig.3 Wave structure of HLLE solver

图4 算例1，屈服强度无穷大时，HLLCE和HLLE的数值结果(a)内能; (b)应力

Fig.4 Numerical results of HLLCE and HLLE for Exp.1 with an infinite yield strength (a) internal energy; (b) deviatoric stress

图5 算例1, 屈服强度Y0=3×108 Pa时，HLLCE和HLLE的数值结果(a)内能; (b)偏应力

Fig.5 Numerical results of HLLCE and HLLE for Exp.1 with Y0=3×108 Pa (a) internal energy; (b) deviatoric stress

图6 算例2，HLLCE和HLLE的数值结果(a)内能; (b)偏应力

Fig.6 Numerical results of HLLCE and HLLE for Exp.2 (a) internal energy; (b)deviatoric stress

图7 算例3：HLLCE、HLLE和HLLCEN的数值结果(a)内能; (b)偏应力

Fig.7 Numerical results of HLLCE, HLLE and HLLCEN for Exp.3 (a) internal energy; (b) deviatoric stress

图8 算例4：HLLCE、HLLE和HLLCEN的数值结果(a)内能; (b)偏应力

Fig.8 Numerical results of HLLCE, HLLE and HLLCEN for Exp.4 (a) internal energy; (b) deviatoric stress

图9 算例5：HLLCE、HLLE和HLLCEN的数值结果(a)内能; (b)偏应力

Fig.9 Numerical results of HLLCE, HLLE and HLLCEN for Exp.5 (a) internal energy; (b) deviatoric stress

图10 泰勒杆长度和能量随时间的变化(a)长度; (b)能量

Fig.10 Variations of Taylor rod length and energy with time for 2D Taylor problem (a) length; (b) energy

图11 泰勒杆密度云图

Fig.11 Density contour of Taylor rod

参考文献 16

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弹塑性问题壁热误差分析及抑制方法

Analyse and Suppression Method of Wall Heating Error for Elastic-Plastic Problem

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