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首页> 外文期刊>International Journal of Heat and Mass Transfer >Analytical solution for the advection-dispersion transport equation in layered media
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Analytical solution for the advection-dispersion transport equation in layered media

机译：层状介质中对流扩散输运方程的解析解

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摘要

The advection-dispersion transport equation with first-order decay was solved analytically for multi-layered media using the classic integral transform technique (CITT). The solution procedure used an associated non-self-adjoint advection-diffusion eigenvalue problem that had the same form and coefficients as the original problem. The generalized solution of the eigenvalue problem for any numbers of layers was developed using mathematical induction, establishing recurrence formulas and a transcendental equation for determining the eigenvalues. The orthogonality property of the eigenfunctions was found using an integrating factor that transformed the non-self-adjoint advection-diffusion eigenvalue problem into a purely diffusive, self-adjoint problem. The performance of the closed-form analytical solution was evaluated by solving the advection-dispersion transport equation for two- and five-layer media test cases which have been previously reported in the literature. Additionally, a solution featuring first-order decay was developed. The analytical solution reproduced results from the literature, and it was found that the rate of convergence for the current solution was superior to that of previously published solutions.
机译：使用经典积分变换技术（CITT）求解多层介质的具有一阶衰减的对流扩散输运方程。求解过程使用了一个相关的非自伴对流扩散特征值问题，该问题的形式和系数与原始问题相同。使用数学归纳法开发了任意数量层的特征值问题的广义解，建立了递归公式和用于确定特征值的超越方程。利用积分因子发现本征函数的正交性，该积分因子将非自伴对流-扩散特征值问题转化为纯扩散自伴问题。通过求解两层和五层介质测试案例的对流扩散输运方程，评估了封闭形式分析解决方案的性能，该案例先前已在文献中进行了报道。此外，还开发了具有一阶衰减的解决方案。该分析解决方案重现了来自文献的结果，并且发现当前解决方案的收敛速度优于以前发布的解决方案。

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