| 瞬态热传导的奇异边界法及其MATLAB实现 |
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| 引用本文： | 李煜冬,王发杰,陈文.瞬态热传导的奇异边界法及其MATLAB实现[J].应用数学和力学,2019,40(3):259-268. |
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| 作者姓名： | 李煜冬 王发杰 陈文 |
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| 作者单位： | 1河海大学 力学与材料学院, 南京 211100;2电动汽车智能化动力集成技术国家地方联合工程研究中心(青岛大学), 山东 青岛 266071;3青岛大学 机电工程学院, 山东 青岛 266071 |
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| 基金项目： | 国家自然科学基金（11802151；11572111；11372097） |
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| 摘 要： | 基于动力学问题时间依赖基本解的奇异边界法是一种无网格边界配点法.该方法引入源点强度因子的概念从而避免了基本解的源点奇异性，具有数学简单、编程容易、精度高等优点.将该方法用于瞬态热传导问题的数值模拟，运用MATLAB实现该问题的数值研究，并创建相应的MATLAB工具箱.针对二维和三维瞬态热传导问题，进行了基于反插值技术和经验公式的奇异边界法MATLAB算例实现.针对支撑圆坯低温瞬态温度场的模拟结果表明，瞬态热传导奇异边界法的MATLAB工具箱具有简单、方便、精确可靠的优点.研究成果有助于发展瞬态热传导的奇异边界法，并为瞬态热传导问题的数值分析和仿真提供了一种简单高效的模拟工具.
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| 关 键 词： | 奇异边界法 反插值技术 经验公式 瞬态热传导 MATLAB |
| 收稿时间： | 2018-08-27 |
MATLAB Implementation of a Singular Boundary Method for Transient Heat Conduction |
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| Affiliation: | 1College of Mechanics and Materials, Hohai University, Nanjing 211100, P.R.China;2National Engineering Research Center for Intelligent Electrical Vehicle Power System(Qingdao University), Qingdao, Shandong 266071, P.R.China;3School of Electromechanic Engineering, Qingdao University, Qingdao, Shandong 266071, P.R.China |
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| Abstract: | The singular boundary method (SBM) based on the time dependent fundamental solutions to dynamic problems is a meshless boundary collocation technique with the merits of easy implementation and mathematical simplicity. This method effectively avoids the singularity of source points through introduction of the origin intensity factor. The SBM was implemented to simulate the transient heat conduction problem via the MATLAB programming, and the MATLAB toolbox was created to provide a simple and efficient tool for the numerical analysis of transient heat conduction problems and actual operating problems. In numerical experiments, 2D and 3D problems were investigated in regular geometrical regions. The method was applied to the solution of the temperature field in the low temperature transient state. The results indicate that the MATLAB toolbox for the SBM with the inverse interpolation technique and the empirical formula is simple, accurate and efficient. |
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