An efficient method for transient heat conduction problems with local nonlinearities based on the quasi-superposition principle
An efficient method for transient heat conduction problems with local nonlinearities based on the quasi-superposition principle
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DOI：
10.1108/hff-02-2022-0087
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发表时间：
2022-07
期刊：
影响因子：
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通讯作者：
Chuanbao Nie;B. Fu;Q. Gao
中科院分区：
文献类型：
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作者：
Chuanbao Nie;B. Fu;Q. Gao
目的研究具有局部辐射边界条件和非线性热源的非线性瞬态热传导问题的有效数值方法。设计/方法/途径基于瞬态热传导的物理特性和绿色函数的分布特性，提出了求解具有局部非线性瞬态热传导问题的拟叠加原理。在此基础上，提出了一种有效的求解方法，该方法可以通过求解一些小结构的非线性问题和一个具有原结构的线性问题来求解原非线性问题。这些问题是相互独立的，可以同时解决的并行计算技术。结果在一个小的时间步长内，非线性热负荷只能引起显着的温度响应的非线性热负荷的位置附近的区域，而其余区域的温度响应非常接近于零。根据上述物理特性，将原非线性问题转化为若干小结构的非线性问题和原结构的线性问题。独创性/价值一个有效的和准确的数值方法，提出了瞬态热传导问题的局部非线性，一些数值例子表明所提出的方法的高效率和精度。
Purpose This paper aims to develop an efficient numerical method for nonlinear transient heat conduction problems with local radiation boundary conditions and nonlinear heat sources. Design/methodology/approach Based on the physical characteristic of the transient heat conduction and the distribution characteristic of the Green’s function, a quasi-superposition principle is presented for the transient heat conduction problems with local nonlinearities. Then, an efficient method is developed, which indicates that the solution of the original nonlinear problem can be derived by solving some nonlinear problems with small structures and a linear problem with the original structure. These problems are independent of each other and can be solved simultaneously by the parallel computing technique. Findings Within a small time step, the nonlinear thermal loads can only induce significant temperature responses of the regions near the positions of the nonlinear thermal loads, whereas the temperature responses of the remaining regions are very close to zero. According to the above physical characteristic, the original nonlinear problem can be transformed into some nonlinear problems with small structures and a linear problem with the original structure. Originality/value An efficient and accurate numerical method is presented for transient heat conduction problems with local nonlinearities, and some numerical examples demonstrate the high efficiency and accuracy of the proposed method.