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. DOI: 10.6052/j.issn.1000-4750.2013.04.0281
引用本文: 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. DOI: 10.6052/j.issn.1000-4750.2013.04.0281
XUE Yan-ni, YANG Hai-tian. A NUMERICAL METHOD TO ESTIMATE TEMPERATURE INTERVALS FOR TRANSIENT HEAT TRANSFER PROBLEMS[J]. Engineering Mechanics, 2014, 31(9): 7-13. DOI: 10.6052/j.issn.1000-4750.2013.04.0281
Citation: XUE Yan-ni, YANG Hai-tian. A NUMERICAL METHOD TO ESTIMATE TEMPERATURE INTERVALS FOR TRANSIENT HEAT TRANSFER PROBLEMS[J]. Engineering Mechanics, 2014, 31(9): 7-13. DOI: 10.6052/j.issn.1000-4750.2013.04.0281

一个瞬态温度场区间上下界估计的数值方法

A NUMERICAL METHOD TO ESTIMATE TEMPERATURE INTERVALS FOR TRANSIENT HEAT TRANSFER PROBLEMS

  • 摘要: 提出一种求解带有区间不确定性参数的瞬态热传导问题的数值方法。利用Taylor展开和区间分析技术,建立温度区间量与不确定参数区间量的确定性关系,然后采用时域分段自适应算法和有限元技术,递推计算温度场的区间半径及区间中值,以估算温度场不确定区间的上下界。自适应计算可根据时间步长的变化,使计算在各离散时段达到给定的计算精度,从而保证整个时域的计算精度。在算例分析中,通过与组合方法、概率方法的比较,说明了所提方法的有效性,并探讨了Taylor展开阶次与计算步长对计算结果的影响。

     

    Abstract: This paper presents a numerical method to solve transient heat transfer problems with interval uncertainty. In virtue of Taylor series expansion and interval analysis, two deterministic equations are derived for the bounds estimation of temperature when thermal parameters are interval variables. A temporally piecewise adaptive algorithm is employed to maintain a steady accuracy over a whole time domain, either for constant or variable sizes of time steps. A numerical example is provided to verify the proposed approach, and a good accordance can be observed by comparing the results given by the combinatorial, probability and proposed approaches. The effects of the order of a Taylor expansion and the size of a time step on the results are discussed.

     

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