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Structured multiblock body-fitted grids solution of transient inverse heat conduction problems in an arbitrary geometry

机译:任意几何结构中的瞬态逆热传导问题的结构化多块体拟合网格解决方案

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摘要

The aim of this study is to develop iterative regularization algorithms based on parameter and function estimation techniques to solve two-dimensional/axisymmetric transient inverse heat conduction problems in curvilinear coordinate system. The multiblock method is used for geometric decomposition of the physical domain into regions with patched-overlapped interface grids. The central finite-difference version of the alternating-direction implicit technique together with structured body-fitted grids is implemented for numerical solution of the direct problem and other partial differential equations derived by inverse analysis. The approach of estimating unknown parameters and functions is iterative inverse analysis algorithms based on the Levenberg-Marquardt method and conjugate gradient methods. The temperature histories are delivered by noisyon-noisy sensors located on the lower boundary of the domain. Three cases are considered, (1) a time-space-varying upper boundary condition, (2) two time-varying heat sources, and (3) a time-varying heat source and a time-space-varying boundary condition, within a two-dimensional/axisymmetric solid body of arbitrary geometry. The simultaneous estimation of two unknown functions is performed to assess the performance of inverse analysis methods to solve complicated inverse heat conduction problems. The results of the present study are compared to those of exact heat sources and boundary condition, and good agreement is achieved. However, the results show that the accuracy of the upper boundary condition identification is dependent on the uncertainty of the measured temperature data, the number of grid points, and the curvature of the geometric configuration as well.
机译:这项研究的目的是开发基于参数和函数估计技术的迭代正则化算法,以解决曲线坐标系中的二维/轴对称瞬态逆导热问题。多块方法用于将物理域几何分解为带有修补重叠界面网格的区域。实现了交替方向隐式技术的中心有限差分形式以及结构化的体拟合网格,以对直接问题和通过反分析得出的其他偏微分方程进行数值求解。估计未知参数和函数的方法是基于Levenberg-Marquardt方法和共轭梯度法的迭代逆分析算法。温度历史记录由位于域下边界的有噪/无噪传感器传递。考虑三种情况:(1)时变上边界条件;(2)两个时变热源;(3)一个时变热源和一个时空边界条件。任意几何形状的二维/轴对称实体。同时进行两个未知函数的估计,以评估反分析方法的性能,以解决复杂的反导热问题。将本研究的结果与精确热源和边界条件的结果进行比较,并取得了良好的一致性。但是,结果表明,上边界条件识别的准确性取决于所测温度数据的不确定性,网格点的数量以及几何构形的曲率。

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