Abstract The Generalized Integral Transform Technique (GITT) is employed in combination with a single domain reformulation strategy and a coupled eigenvalue problem expansion base to construct analytical or hybrid numerical-analytical solutions for flow and transport in fractured porous media. The problem formulation and provided formal solutions encompass both continuum (multi-porosity/multi-permeability) and discrete (fracture-matrix interaction) models for heterogeneous porous media. The single domain representation is written with the aid of space variable coefficients, that account for the abrupt physical properties and source terms transitions across the different subregions. The aim is to provide an unified formalism that includes a wide class of problems in fluid flow, heat and mass transfer in heterogeneous media, with the integral transformation process for the potentials (pressure, velocities, temperature, or concentrations) being applied over the whole physical domain at once, thus markedly reducing the mathematical manipulations. The space variable coefficients are then carried on to the eigenvalue problem formulation which provides the base for the eigenfunction expansion. In addition, a coupled eigenvalue problem alternative is proposed, which is particularly useful in dealing with multi-porosity/multi-permeability flow and transport models, collapsing the multiple coupled potentials equations into one single integral transformation process. Two representative applications are briefly considered, one dealing with contaminant transport with discrete fracture-matrix interaction in layered porous media and the other related to dual porosity/dual permeability model of flow in unsaturated soils.

中文翻译：

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裂隙非均质多孔介质离散和连续模型中流动和输运的积分变换

摘要 采用广义积分变换技术（GITT），结合单域重构策略和耦合特征值问题扩展基础，构建裂隙多孔介质中流动和输运的解析解或混合数值解析解。问题表述和提供的正式解决方案包括非均质多孔介质的连续模型（多孔隙度/多渗透率）和离散（裂缝-基质相互作用）模型。单域表示是在空间变量系数的帮助下编写的，它解释了跨越不同子区域的突然物理特性和源项转换。目的是提供一个统一的形式体系，其中包括非均质介质中流体流动、传热和传质方面的各种问题，将势（压力、速度、温度或浓度）的积分转换过程一次应用于整个物理域，从而显着减少了数学运算。然后将空间变量系数用于特征值问题公式，该公式为特征函数展开提供基础。此外，还提出了一种耦合特征值问题替代方案，它在处理多孔隙度/多渗透率流动和输运模型、将多个耦合势方程分解为一个单一的积分转换过程时特别有用。简要考虑两个具有代表性的应用，