Solving advection-diffusion-reaction problems in layered media using the Laplace transform
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We derive a semi-analytical Laplace-transform based solution to the one-dimensional linear advection-diffusion-reaction equation in a layered medium. Our solution approach involves introducing unknown functions representing the diffusive 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-diffusion-reaction equation, a finite medium comprising an arbitrary number of layers, continuity of concentration and diffusive flux at the interfaces between adjacent layers and transient boundary conditions of arbitrary type at the two boundaries. Our derived semi-analytical solution extends and addresses deficiencies of existing Laplace-transform based solutions in a layered medium, which consider diffusion or reaction-diffusion only. Code implementing our semi-analytical solution is provided 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.
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