移动边界问题的时空域正则区域迭代配点法

doi:10.19596/j.cnki.1001-246x.8177

计算物理 ›› 2021, Vol. 38 ›› Issue (1): 16-24.DOI: 10.19596/j.cnki.1001-246x.8177

移动边界问题的时空域正则区域迭代配点法

王兆清¹, 钱航¹, 李金²

1. 山东建筑大学理学院, 山东济南 250101;
2. 华北理工大学理学院, 河北唐山 063200

收稿日期:2019-11-27 修回日期:2020-03-03 出版日期:2021-01-25 发布日期:2021-01-25
通讯作者: 李金,E-mail:281379913@qq.com
作者简介:王兆清(1965-),男,博士,教授,从事工程数值分析方法研究,E-mail:wangzhaoqing@sdjzu.edu.cn
基金资助:
山东省自然科学基金省属高校优青项目（ZR2016JL006）和河北省自然科学基金面上项目（A2019209533）资助

Regular Domain Iterative Collocation Method in Space-Time Region for Moving Boundary Problems

WANG Zhaoqing¹, QIAN Hang¹, LI Jin²

1. School of Science, Shandong Jianzhu University, Jinan, Shandong 250101, China;
2. School of Science, North China University of Science and Technology, Tangshan, Hebei 063200, China

Received:2019-11-27 Revised:2020-03-03 Online:2021-01-25 Published:2021-01-25

摘要/Abstract

摘要： 考虑热传导方程的移动边界问题，其定解区域随着时间而变化。构造一种时空域上的高精度数值算法求解1+1维移动边界问题。在时空域上假设一个初始移动边界位置，构成移动边界问题的不规则计算区域，选择一个适当的正则区域（矩形区域）完全覆盖所计算的不规则区域，在正则区域上利用移动边界约束条件和固定边界条件，采用时空域重心插值配点法求解1+1维扩散方程，得到正则区域上扩散方程数据。采用二维重心插值计算假设移动边界上函数关于时间偏导数的数值，进而利用一维重心插值配点法求解移动界面控制常微分方程，得到新的假设移动界面位置。重复上述流程，最终得到问题的数值解和移动界面的最终位置。通过典型数值算例验证所建立的数值方法的有效性和数值计算精度。

关键词: 移动边界问题, 重心插值, 时空域配点法, 正则区域法, 热传导方程

Abstract: The governing equation of moving boundary problem is heat conductive equation. Its definite solution domain varies with time. Highly precision numerical algorithms on space-time domain were presented to solve 1+1 dimensional moving boundary problems. An initial moving boundary was given to form an irregular physical domain, and a regular region (a rectangular in Cartesian coordinate system) was chosen to cover the irregular physical domain. The heat equation was numerically computed with a barycentric interpolation collocation method (BICM) on space-time regular region with fixed and moving boundary conditions and initial condition to obtain numerical data in regular region. The data on moving boundary of physical domain were computed with barycentric interpolation. Then, the governing equation of moving boundary was solved with BICM to recover a new moving boundary. Repeat the process, numerical data of temperature and final moving boundary position were given. Numerical examples illustrate effectiveness and accuracy of the method.

Key words: moving boundary problem, barycentric interpolation, space-time collocation method, regular region method, heat conductive equation

中图分类号:

O411.3

王兆清, 钱航, 李金. 移动边界问题的时空域正则区域迭代配点法[J]. 计算物理, 2021, 38(1): 16-24.

WANG Zhaoqing, QIAN Hang, LI Jin. Regular Domain Iterative Collocation Method in Space-Time Region for Moving Boundary Problems[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2021, 38(1): 16-24.

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移动边界问题的时空域正则区域迭代配点法

Regular Domain Iterative Collocation Method in Space-Time Region for Moving Boundary Problems

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