论文标题
多层多孔介质中的耦合多物流对流方程的广义半分析溶液
Generalized semi-analytical solution for coupled multispecies advection-dispersion equations in multilayer porous media
论文作者
论文摘要
地球地下中的多种污染物传输通常是使用通过一阶反应耦合的对流 - 分散方程建模的。对于此类问题的分析和半分析溶液是高度追捧的，但目前仅限于一种物种，同质培养基，某些反应网络，特定的边界条件或其组合。在本文中，我们为异质分层培养基和一般一阶反应网络的情况开发了半分析溶液。我们的方法结合了一种转换方法，将多物种方程与最近开发的半分析解决方案与单物种对流 - 分散反应方程式中的新分析解决方案进行了结合。通用解决方案对于任意数量的物种和层，在入口和出口处的普通robin型条件有效，并适应跨层之间的两个不同的延迟因子或物种之间不同的延迟因子。提出了四个测试案例，以证明与先前发表的结果以及通过有限体积离散化获得的数值结果一致的溶液方法。实施广义半分析解决方案的MATLAB代码可提供。
Multispecies contaminant transport in the Earth's subsurface is commonly modelled using advection-dispersion equations coupled via first-order reactions. Analytical and semi-analytical solutions for such problems are highly sought after but currently limited to either one species, homogeneous media, certain reaction networks, specific boundary conditions or a combination thereof. In this paper, we develop a semi-analytical solution for the case of a heterogeneous layered medium and a general first-order reaction network. Our approach combines a transformation method to decouple the multispecies equations with a recently developed semi-analytical solution for the single-species advection-dispersion-reaction equation in layered media. The generalized solution is valid for arbitrary numbers of species and layers, general Robin-type conditions at the inlet and outlet and accommodates both distinct retardation factors across layers or distinct retardation factors across species. Four test cases are presented to demonstrate the solution approach with the reported results in agreement with previously published results and numerical results obtained via finite volume discretisation. MATLAB code implementing the generalized semi-analytical solution is made available.
