On the numerical simulation of diffusion-controlled reactions under local equilibrium conditions

To estimate the interfacial velocity in a multicomponent moving boundary problem, existing procedures require an interative technique to be used if a sharp interface method is employed. The need to use an interative technique can cause convergence problems; these become more frequent as more components are added. In this paper, two new methods are suggested which allow the velocity of a phase interface to be evaluated directly from the fluxes of the components under the assumption of local equilibrium. The methods assume that the interface has a fixed width in which the incoming and outgoing components are distributed in a way that moves the interface while maintaining local equilibrium. Example simulations are presented and results are in good agreement with established front-tracking simulation software (DICTRA); moreover, the superior convergence of the new methods is demonstrated.