Abstract Existing closed-form solutions of contaminant transport problems are limited by the mathematically convenient assumption of uniform flow. These solutions cannot be used to investigate contaminant transport in coastal aquifers where seawater intrusion induces a variable velocity field. An adaptation of the Fourier-Galerkin method is introduced to obtain semi-analytical solutions for contaminant transport in a confined coastal aquifer in which the saltwater wedge is in equilibrium with a freshwater discharge flow. Two scenarios dealing with contaminant leakage from the aquifer top surface and contaminant migration from a source at the landward boundary are considered. Robust implementation of the Fourier-Galerkin method is developed to efficiently solve the coupled flow, salt and contaminant transport equations. Various illustrative examples are generated and the semi-analytical solutions are compared against an in-house numerical code. The Fourier series are used to evaluate relevant metrics characterizing contaminant transport such as the discharge flux to the sea, amount of contaminant persisting in the groundwater and solute flux from the source. These metrics represent quantitative data for numerical code validation and are relevant to understand the effect of seawater intrusion on contaminant transport. It is observed that, for the surface contamination scenario, seawater intrusion limits the spread of the contaminant but intensifies the contaminant discharge to the sea. For the landward contamination scenario, moderate seawater intrusion affects only the spatial distribution of the contaminant plume while extreme seawater intrusion can increase the contaminant discharge to the sea. The developed semi-analytical solution presents an efficient tool for the verification of numerical models. It provides a clear interpretation of the contaminant transport processes in coastal aquifers subject to seawater intrusion. For practical usage in further studies, the full open source semi-analytical codes are made available at the website https://lhyges.unistra.fr/FAHS-Marwan .

中文翻译：

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沿海含水层变速场污染物运移的半解析解

摘要 污染物运输问题的现有封闭形式解决方案受到数学上方便的均匀流假设的限制。这些解决方案不能用于研究沿海含水层中的污染物迁移，在这些含水层中，海水入侵会引起变速场。引入了傅立叶-伽辽金方法的改进，以获得污染物在受限制的沿海含水层中传输的半解析解，其中盐水楔与淡水排放流处于平衡状态。考虑了两种处理从含水层顶面泄漏的污染物和污染物从向陆边界源迁移的情景。傅立叶-伽辽金方法的稳健实施旨在有效求解耦合流动、盐分和污染物传输方程。生成了各种说明性示例，并将半解析解与内部数字代码进行比较。傅里叶级数用于评估表征污染物迁移的相关指标，例如向海洋的排放通量、地下水中持续存在的污染物量和来自源头的溶质通量。这些指标代表数字代码验证的定量数据，与了解海水入侵对污染物传输的影响有关。据观察，对于地表污染场景，海水入侵限制了污染物的传播，但加剧了污染物向海洋的排放。对于向陆污染的情景，适度的海水入侵只会影响污染物羽流的空间分布，而极端的海水入侵会增加污染物排放到海洋中。开发的半解析解决方案为验证数值模型提供了一种有效的工具。它清楚地解释了受海水入侵影响的沿海含水层中污染物的迁移过程。对于进一步研究的实际使用，完整的开源半分析代码可在网站 https://lhyges.unistra.fr/FAHS-Marwan 上获得。