入口边界条件指数衰减的一维平流扩散方程解的注记

IF 3.3 Q2 MULTIDISCIPLINARY SCIENCES

Scientific African Pub Date : 2025-09-12 DOI:10.1016/j.sciaf.2025.e02956

Joseph K. Ansong, Ferdinard Obeng-Forson, Vincent T. Teyekpiti

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引用次数: 0

摘要

给出了入口边界条件呈指数衰减且出口梯度为非零的一维平流扩散方程的解析解。利用拉普拉斯变换方法推导了该问题的解，并通过显式有限差分格式得到了数值解进行比较。数值结果与解析解吻合较好。此外，这项工作纠正了先前发表的解析解（van Genuchten和Alves， 1982）中的一个错误，该解析解在出口处应用了零梯度条件。

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A note on the solution to a 1D advection–diffusion equation with exponentially decaying inlet boundary condition

An analytical solution is presented for a one-dimensional advection–diffusion equation (ADE) with an exponentially decaying inlet boundary condition and a non-zero gradient at the outlet. The solution is derived using the Laplace transform method, and a numerical solution is obtained through an explicit finite difference scheme for comparison. The numerical results show good agreement with the analytical solution. Additionally, this work corrects an error in a previously published analytical solution (van Genuchten and Alves, 1982), which applied a zero-gradient condition at the outlet.

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