Discretization and Solver Methods with Analytical Characteristic Methods for Advection-Diffusion Reaction Equations and 2D Applications

Our studies are motivated by a desire to model long-time simulations of possible scenarios for waste disposal. We present transport of pollutants through ground water flowing through rocks or sand regarded as porous media. The models, including the conservation of mass and momentum for velocity and the porous media, are in accordance with Darcy's low. Numerical methods are developed for solving the arising systems of convection-diffusion-dispersion reaction equations, and the received results of several discretization methods are presented. In the numerical methods, we use large time steps to achieve long simulation times of about 10,000 years. We propose higher-order discretization methods, which allow us to use large time steps without losing accuracy. Operator splitting methods allow the decomposition of the multiphysical and multidimensional equation. Simpler physical and one-dimensional equations are obtained and can be discretized with higher-order methods. We obtain more effective solver methods with an underlying physical operator-splitting method. In the numerical example we simulate a radioactive waste disposal with underlying flowing groundwater that is solved by a density-driven flow model. The transport and reaction simulations for the decay chains are presented in 2D realistic domains, and we discuss the received results. Finally we present our conclusions and discuss possible further work.