工程力学 ›› 2019, Vol. 36 ›› Issue (3): 33-39.doi: 10.6052/j.issn.1000-4750.2018.01.0003

• 基本方法 • 上一篇    下一篇

时域径向积分边界元法在平面单相凝固问题中的应用

左冲, 姚鸿骁, 姚伟岸   

  1. 工业装备结构分析国家重点实验室, 大连理工大学, 大连, 辽宁 116024
  • 收稿日期:2018-01-02 修回日期:2018-07-05 出版日期:2019-03-29 发布日期:2019-03-16
  • 通讯作者: 姚伟岸(1963-),男,辽宁人,教授,博士,博导,主要从事计算力学研究(E-mail:ywa@dlut.edu.cn). E-mail:ywa@dlut.edu.cn
  • 作者简介:左冲(1993-),男,湖北人,硕士生,主要从事计算力学研究(E-mail:zuoyongchong@163.com);姚鸿骁(1991-),男,山东人,博士生,主要从事计算力学研究(E-mai:yaohongxiao0314@126.com)
  • 基金资助:
    国家自然科学基金项目(11672064)

THE APPLICATION OF THE TIME DOMAIN RADIAL INTEGRAL BOUNDARY ELEMENT METHOD IN 2D ONE-PHASE SOLIDIFICATION

ZUO Chong, YAO Hong-xiao, YAO Wei-an   

  1. State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian, Liaoning 116024, China
  • Received:2018-01-02 Revised:2018-07-05 Online:2019-03-29 Published:2019-03-16

摘要: 该文将时域精细积分边界元方法与界面追踪法相结合,给出平面单相凝固热传导问题的一个有效数值分析方法。首先,利用稳态热传导问题的基本解和径向积分法给出瞬态传热问题的边界积分方程,并采用精细积分方法求解离散的微分方程组,获得相变界面的热流密度。然后应用相变界面上的能量守恒方程,采用界面追踪法来预测相变边界的移动位置,从而给出相关问题数值模拟的结果。最后,为验证该文方法的有效性,给出两个数值算例并与解析解进行了对比。结果表明,该文方法具有较高的求解精度,是求解相变热传导问题的一种有效数值方法。

关键词: 边界元法, 相变凝固, 瞬态热传导, 界面追踪法, 径向积分法, 精细积分法

Abstract: A combined approach of the precise integration boundary element method and the front-tracking method is presented for thermal conduction problems with one-phase solidification. Firstly, the boundary integral equation of transient thermal conduction is given by using the fundamental solution of steady-state thermal conduction problems and radial integration method. The precise integration method is applied to solve the discrete differential equations for obtaining the heat flux density of the moving boundary. Then the energy conservation equation of the moving boundary and the front-tracking method are applied to predict the position of the moving boundary, and the results of numerical simulations are obtained. To validate the proposed method, two typical examples are given and compared with the analytical solutions. The results show that the proposed method has a high accuracy and is an effective numerical method for solving thermal conduction problems with phase solidification.

Key words: boundary element method, phase solidification, transient thermal conduction, front-tracking, radial integration method, precise integration method

中图分类号: 

  • O241.8
[1] Chessa J, Smolinski P, Belytschko T. The extended finite element method (XFEM) for solidification problems[J]. International Journal for Numerical Methods in Engineering, 2002, 53(8):1959-1977.
[2] Zhang L, Rong Y M, Shen H F, et al. Solidification modeling in continuous casting by finite point method[J]. Journal of Materials Processing Technology, 2007, 192(5):511-517.
[3] Muhieddine M, Canot E, March R. Various approaches for solving problems in heat conduction with phase change[J]. International Journal on Finite Volumes, 2009, 6(1):1-20.
[4] 李海梅, 顾元宪, 申长雨. 平面相变热传导问题等效热容法的有限元解[J]. 大连理工大学学报, 2000, 40(1):45-48. Li Haimei, Gu Yuanxian, Shen Changyu. Finite element solution of heat transfer with planar phase change by equivalent heat capacity method[J]. Journal of Dalian University of Technology, 2000, 40(1):45-48. (in Chinese)
[5] Yang H T, He Y Q. Solving heat transfer problems with phase change via smoothed effective heat capacity and element-free Galerkin methods[J]. International Communications in Heat and Mass Transfer, 2010, 37(4):385-392.
[6] 王海涛, 姚振汉. 快速多极边界元法在大规模传热分析中的应用[J]. 工程力学, 2008, 25(9):23-27. Wang H T, Yao Z H. Application of fast multipole boundary element method on large scale thermal analysis[J]. Engineering Mechanics, 2008, 25(9):23-27. (in Chinese)
[7] Liu J, Lu W Q. Numerical simulation of non-isothermal phase change problem using a DRBEM with augmented items[J]. Journal of Engineering Thermophysics, 2006, 36(7):408-416.
[8] Gao X W. The radial integration method for evaluation of domain integrals with boundary-only discretization[J]. Engineering Analysis with Boundary Elements, 2002, 26(10):905-916.
[9] Yang K, Gao X W. Radial integration BEM for transient heat conduction problems[J]. Engineering Analysis with Boundary Elements, 2010, 34(6):557-563.
[10] Jesus L J M, Cimini C A, Albuquerque E L. Application of the radial integration method into dynamic formulation of anisotropic shallow shells using boundary element method[J]. Key Engineering Materials, 2015, 627(9):465-468.
[11] 邓琴, 李春光, 王水林, 等. 无域积分的弹塑性边界元法的非线性互补方法[J]. 工程力学, 2012, 29(7):49-55. Deng Qin, Li Chunguang, Wang Shuilin, et al. Nonlinear complementarity approach for elastoplastic bem without internal cell[J]. Engineering Mechanics, 2012, 29(7):49-55. (in Chinese)
[12] Yu B, Yao W A. A precise time-domain expanding boundary-element method for solving three-dimensional transient heat conduction problems with variable thermal conductivity[J]. Numerical Heat Transfer Part B Fundamentals, 2014, 66(5):422-445.
[13] Yu B, Yao W A, Zhou H L, et al. Precise time-domain expanding BEM for solving non-fourier heat conduction problems[J]. Numerical Heat Transfer Part B Fundamentals, 2015, 68(6):511-532.
[14] 钟万勰. 子域精细积分及偏微分方程数值解[J]. 计算结构力学及其应用, 1995, 12(3):253-260. Zhong Wanxie. Subdomain Precise integration method and numerical solution of partial differential equations[J]. Chinese Journal of Computational Mechanics, 1995, 12(3):253-260. (in Chinese)
[15] Zabaras N, Mukherjee S. An analysis of solidification problems by the boundary element method[J]. International Journal for Numerical Methods in Engineering, 1987, 24(10):1879-1900.
[16] Gao X W. A meshless BEM for isotropic heat conduction problems with heat generation and spatially varying conductivity[J]. International Journal for Numerical Methods in Engineering, 2006, 66(9):1411-1431.
[17] O'Neill K. Boundary integral equation solution of moving boundary phase change problems[J]. International Journal for Numerical Methods in Engineering, 1983, 19(12):1825-1850.
[1] 巴振宁, 彭琳, 梁建文, 黄棣旸. 任意多个凸起地形对平面P波的散射[J]. 工程力学, 2018, 35(7): 7-17,23.
[2] 巴振宁, 严洋, 梁建文, 张艳菊. 基于TI介质模型的凸起地形对平面SH波的放大作用[J]. 工程力学, 2017, 34(8): 10-24.
[3] 王冬, 刘中宪, 武凤娇, 刘蕾. 弹性波三维散射快速多极子间接边界元法求解[J]. 工程力学, 2017, 34(1): 33-44.
[4] 李青宁, 尹俊红, 张瑞杰, 韩春. 基于精细积分法的结构碰撞动力系数谱研究[J]. 工程力学, 2016, 33(3): 161-168.
[5] 姚振汉. 真实梁板壳局部应力分析的高性能边界元法[J]. 工程力学, 2015, 32(8): 8-8.
[6] 刘中宪,唐河仓,王冬. 弹性波二维散射快速多极子间接边界元法求解[J]. 工程力学, 2015, 32(5): 6-7.
[7] 薛燕妮,杨海天. 一个瞬态温度场区间上下界估计的数值方法[J]. 工程力学, 2014, 31(9): 7-13.
[8] 陈磊磊, 陈海波, 郑昌军, 徐延明. 基于有限元与宽频快速多极边界元的二维流固耦合声场分析[J]. 工程力学, 2014, 31(8): 63-69.
[9] 黄拳章, 强洪夫, 郑小平, 姚振汉. 混合夹杂问题的边界元法[J]. 工程力学, 2014, 31(11): 17-24.
[10] 杜宪亭,夏禾,李慧乐,崔堃鹏. 基于改进高斯精细积分法的车桥耦合振动分析框架[J]. 工程力学, 2013, 30(9): 171-176.
[11] 李秀梅,吴锋,张克实. 结构动力微分方程的一种高精度摄动解[J]. 工程力学, 2013, 30(5): 8-12.
[12] 邓琴, 李春光, 王水林, 葛修润. 无域积分的弹塑性边界元法的非线性互补方法[J]. 工程力学, 2012, 29(7): 49-55.
[13] 司炜, 许强. 二维新型快速多极虚边界元配点法[J]. 工程力学, 2012, 29(10): 52-56,62.
[14] 刘 龙;轩福贞;董达善. 脉动流作用下粘弹性直管动力学特性分析[J]. 工程力学, 2011, 28(10): 41-045.
[15] 张志超;张亚辉;林家浩. 水平地震下列车过桥的非平稳随机响应及其极值估计[J]. 工程力学, 2011, 28(1): 178-185.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!
X

近日,本刊多次接到来电,称有不法网站冒充《工程力学》杂志官网,并向投稿人收取高额费用。在此,我们郑重申明:

1.《工程力学》官方网站是本刊唯一的投稿渠道(原网站已停用),《工程力学》所有刊载论文必须经本刊官方网站的在线投稿审稿系统完成评审。我们不接受邮件投稿,也不通过任何中介或编辑收费组稿。

2.《工程力学》在稿件符合投稿条件并接收后会发出接收通知,请作者在接到版面费或审稿费通知时,仔细检查收款人是否为“《工程力学》杂志社”,千万不要汇款给任何的个人账号。请广大读者、作者相互转告,广为宣传!如有疑问,请来电咨询:010-62788648。

感谢大家多年来对《工程力学》的支持与厚爱,欢迎继续关注我们!

《工程力学》杂志社

2018年11月15日