Domain decomposition with Robin boundary conditions across a phase interface

Abstract

Domain decompositions are typically pursued in order to split up large elliptic boundary-value problems into a set of smaller problems that can each be solved separately, with the solution to the larger problem obtained through iterative application of inter-domain boundary conditions. Here we review a related problem that arises in the study of unsteady advection-diffusion with two solvent phases. A boundary iteration scheme is devised and tested within the context of an idealised Poisson problem. The method is then used in the simulation of capillary chromatography and the results compared to an available analytical solution.