62 citations · 405 across the 26 of their papers we have counts for
5 papers · 1 filter
New semi-analytical solutions for advection-dispersion equations in multilayer porous media
Elliot J. Carr
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 solu…
A fast algorithm for semi-analytically solving the homogenization boundary value problem for block locally-isotropic heterogeneous media
Nathan G. March, Elliot J. Carr, Ian W. Turner
Direct numerical simulation of diffusion through heterogeneous media can be difficult due to the computational cost of resolving fine-scale heterogeneities. One method to overcome…
Finite volume schemes for multilayer diffusion
Nathan G. March, Elliot J. Carr
This paper focusses on finite volume schemes for solving multilayer diffusion problems. We develop a finite volume method that addresses a deficiency of recently proposed finite vo…
Semi-analytical solution of multilayer diffusion problems with time-varying boundary conditions and general interface conditions
Elliot J. Carr, Nathan G. March
We develop a new semi-analytical method for solving multilayer diffusion problems with time-varying external boundary conditions and general internal boundary conditions at the int…
Calculating how long it takes for a diffusion process to effectively reach steady state without computing the transient solution
Elliot J. Carr
Mathematically, it takes an infinite amount of time for the transient solution of a diffusion equation to transition from initial to steady state. Calculating a \textit{finite} tra…