Papers › New semi-analytical solutions for advection-dispersion equations in multilayer porous media
New semi-analytical solutions for advection-dispersion equations in multilayer porous media
Elliot J. Carr
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
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.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections