A simple numerical approach for assessing coupled transport processes in partitioning systems

Recent concepts in the solution of multidomain equation systems are applied to the problem of distinct transport processes coupled over geometrically disjoint domains. The (time dependent) transport equations for the composite system are solved using a simple domain decomposition approach, with parallel implementations of detailed Schwarz balances for the system subdomain interfaces. An existing numerical partial differential equation (PDE) solver is coupled with the interface algorithms to provide a code capable of handling a wide range of dynamical equations within the subdomains. Interface partitioning conditions corresponding to sharply discontinuous Dirichlet constraints, and to (discontinuous) rate-limited Neumann constraints are also incorporated into the code. A variety of transport operators can be handled simply by altering the equation system code block. The code is validated against analytical solutions for representative parabolic transport equations including recent solutions for diffusive transport in partitioning laminates, useful for describing the movement of chemical species in composite materials. The code is then applied to an example problem of coupled multiphase chemical transport in a variably saturated soil column with a low-permeability capping.