Discretization 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 a waste disposal. 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. In the numerical example we simulate a realistic radioactive waste disposals with underlying flowing groundwater.