Numerical solution of two-dimensional convection-diffusion-adsorption problems using an operator splitting scheme

In this paper, an efficient numerical method for solving two-dimensional convection-dispersion-adsorption problems is introduced. The method is applied to a practical problem of soil parameters reconstruction using dual-well tests. We consider a general mathematical model which includes contaminant transport, mechanical dispersion and molecular diffusion and adsorption in both equilibrium and non-equilibrium modes. The problem is solved using a numerical scheme based on operator splitting approach - in each time step we solve separately the transport, dispersion and non-equilibrium sorption part. The original half-plane domain is transformed to a rectangle using an orthogonal transformation, which makes the transport problem one-dimensional and its solution can be then found in an analytical form. The dispersion part is solved using finite volume method. For the system of ODE's representing adsorption we derive an implicit scheme. Some computational aspects of the problem are discussed and various results of numerical experiments are shown.