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Numerical analysis of an advective diffusion domain coupled with a diffusive heat source

机译：对流扩散域与扩散热源耦合的数值分析

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摘要

This paper presents a formulation of the boundary element method (BEM) for the study of heat diffusion and advective effect in isotropic and homogeneous media. The proposed formulation has a time independent fundamental solution obtained from the two-dimensional Laplace equation. Consequently, the formulation is called D-BEM since it has domain integrals in the basic integral equation. The first order time derivative that appears in the integral equations is approximated by a backward finite difference scheme. Homogeneous subregions are considered in the analysis in a specific model simulating a nonuniform flow passing by a circular obstacle under internal heat generation. Results from numerical models are compared with the available analytical solutions. The correlation estimator R~2 is employed to validate the numerical model and to demonstrate the accuracy of the proposed formulation.
机译：本文提出了一种边界元方法（BEM）的公式，用于研究在各向同性和均质介质中的热扩散和对流效应。所提出的公式具有从二维拉普拉斯方程获得的与时间无关的基本解。因此，该公式称为D-BEM，因为它在基本积分方程中具有域积分。积分方程中出现的一阶时间导数通过后向有限差分方案近似。在特定模型中的分析中考虑了同质子区域，该模型模拟了内部热量产生时绕过圆形障碍物的不均匀流动。将数值模型的结果与可用的分析解决方案进行比较。相关估计器R〜2用于验证数值模型并证明所提出公式的准确性。

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