Discretization methods with analytical characteristic methods for advection-diffusion-reaction equations and 2D applications. (English) Zbl 1180.35026

The present 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 system of convection-diffusion-dispersion-reaction equations, and the received results of several discretization methods are presented. The authors concentrate on linear reaction systems, which can be solved analytically. In the numerical methods, they use large time-steps to achieve long simulation times of about 10000 years. High-order discretization methods, which allow us to use large time-steps without losing accuracy are proposed. By decoupling of a multi-physical and multi-dimensional equation, simpler physical and one-dimensional equations are obtained and can be discretized with high-order methods. The results can then be coupled with an operator-splitting method. One discusses benchmark problems given in the literature and real-life applications. A radioactive waste disposal with underlying flowing groundwater is simulated. The transport and reaction simulations for the decay chains are presented in 2D realistic domains, and the received results are discussed. Finally, some conclusions and ideas for further works are presented.


35A35 Theoretical approximation in context of PDEs
35K15 Initial value problems for second-order parabolic equations
35K57 Reaction-diffusion equations
47F05 General theory of partial differential operators
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs


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