论文标题
多层培养基中的新的半分析溶液的半分析解决方案
New semi-analytical solutions for advection-dispersion equations in multilayer porous media
论文作者
论文摘要
使用Laplace变换得出了用于对流多孔介质中溶质转运的对流散至反应方程的新的半分析解决方案。我们的解决方案方法涉及在相邻层之间的界面上引入代表分散通量的未知函数，从而使多层问题在拉普拉斯域中的每个层上分别求解，然后再倒回时域。该衍生的解决方案适用于最通用的线性对流 - 分散反应方程，一种有限的介质，其中包含任意层的层，浓度的连续性和相邻层之间接口的连续性以及在入口和出口处任意类型的瞬态边界条件的接口。派生的半分析溶液扩展并解决了分层介质中现有分析溶液的缺陷，该培养基仅考虑类似过程，例如扩散或反应 - 扩散和/或需要对复杂的非线性超越方程的溶液来评估溶液表达。提供了实施我们的半分析解决方案的代码，并将其应用于测试案例的选择，其结果与标准数值解决方案和文献中可用的其他分析结果非常吻合。
A new semi-analytical solution to the advection-dispersion-reaction equation for modelling solute transport in layered porous media is derived using the Laplace transform. Our solution approach involves introducing unknown functions representing the dispersive flux at the interfaces between adjacent layers, allowing the multilayer problem to be solved separately on each layer in the Laplace domain before being numerically inverted back to the time domain. The derived solution is applicable to the most general form of linear advection-dispersion-reaction equation, a finite medium comprising an arbitrary number of layers, continuity of concentration and dispersive flux at the interfaces between adjacent layers and transient boundary conditions of arbitrary type at the inlet and outlet. The derived semi-analytical solution extends and addresses deficiencies of existing analytical solutions in a layered medium, which consider analogous processes such as diffusion or reaction-diffusion only and/or require the solution of complicated nonlinear transcendental equations to evaluate the solution expressions. Code implementing our semi-analytical solution is supplied and applied to a selection of test cases, with the reported results in excellent agreement with a standard numerical solution and other analytical results available in the literature.
