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首页> 外文期刊>International Journal of Heat and Mass Transfer >An iterative finite-element algorithm for solving two-dimensional nonlinear inverse heat conduction problems
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An iterative finite-element algorithm for solving two-dimensional nonlinear inverse heat conduction problems

机译：求解二维非线性逆导热问题的迭代有限元算法

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摘要

It is often useful to determine temperature and heat flux in multidimensional solid domains of arbitrary shape with inaccessible boundaries. In this study, an effective algorithm for solving boundary inverse heat conduction problems (IHCPs) is implemented: transient temperatures on inaccessible boundaries are estimated from redundant simulated measurements on accessible boundaries. A nonlinear heat equation is considered, where some of the material properties are dependent on temperature. The IHCP is reformulated as an optimization problem. The resulting functional is iteratively minimized using a conjugate gradient method together with an adjoint (dual) problem approach. The associated partial differential equations are solved using the finite-element package FEniCS. Tikhonov regularization is introduced to mitigate the ill-posedness of the IHCP. The accuracy of the implemented algorithm is assessed by comparing the solutions to the IHCP with the correct temperature values, on the inaccessible boundaries. The robustness of our method is tested by adding Gaussian noise to the initial conditions and redundant boundary data in the inverse problem formulation. A mesh independence study is performed. (C) 2018 Elsevier Ltd. All rights reserved.
机译：确定边界不可访问的任意形状的多维实体域中的温度和热通量通常很有用。在这项研究中，实现了一种解决边界逆导热问题（IHCP）的有效算法：无法访问边界上的瞬态温度是通过对可访问边界上的冗余模拟测量值进行估算的。考虑了非线性热方程，其中某些材料特性取决于温度。 IHCP被重新表述为优化问题。使用共轭梯度方法和伴随（对偶）问题方法，将生成的函数迭代最小化。相关的偏微分方程使用有限元软件包FEniCS求解。引入Tikhonov正则化以减轻IHCP的不适。通过在难以接近的边界上将IHCP的解与正确的温度值进行比较，可以评估所实现算法的准确性。通过将高斯噪声添加到初始条件和逆问题公式中的冗余边界数据来测试我们方法的鲁棒性。进行网格独立性研究。 （C）2018 Elsevier Ltd.保留所有权利。

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