Solution of contaminant transport with equilibrium and non-equilibrium adsorption

In this paper we present a numerical approximation scheme for the solution of contaminant transport problems with diffusion and adsorption in equilibrium and non-equilibrium mode. The method is based on time stepping and operator splitting. The non-linear transport is solved semi-analytically via the multiple Riemann problem, the non-linear diffusion by a finite volume method and by Newton's type of linearisation, and finally the reaction part, incorporating the non-equilibrium adsorption, is transformed to an integral equation which is solved numerically using time discretization. Various results of numerical experiments are shown, and the method is applied to the practical dual-well problem.