Analytical Solutions for Convection-Diffusion-Dispersion-Reaction-Equations with Different Retardation-Factors and Applications in 2d and 3d
Institut für Mathematik
Our motivation to this paper came from a model simulating a wastedisposal embedded in an overlying rock. The main problem for our model are the large scales that occurred due the coupled reaction terms of our underlying system of convection-diffusion-dispersion-reactionequations. The developed methods allowed a computation over a large simulation period of more than 10000 years. Therefore we construct discretization methods of higher order, which allow large-time-steps without loss of accuracy. Based on operator-splitting methods we decouple the complex equations in simpler equations and use adequate methods to solve each equation separately. For the explicit parts that are the convection-reaction-equations we use finite-volume methods based on flux-methods with embedded analytical solutions. Whereas for the implicit parts that are the diffusion-dispersion-equations we use finitevolume methods with central discretizations. We analyze the splittingerror and the discretization error for our methods. The main part of the paper consists of the applications of our methods done with our underlying program-tool R3T. We introduced the main concepts of the program-tool that is based on the software-toolbox UG. The testexamples and benchmark problems for verifying our discretization- and solver-methods with respect to the physical behavior are presented. The benchmark-problems are the test for different material-parameters and confirm the valuation of the methods. Based on the verification of our test-problem we present the realistic model-problem of a waste-disposal in 2d with large decay-chains reacted and transported in a porous media with an underlying flowing groundwater. For the prediction of possible waste-disposals a computation with different located waste-locations is discussed. The parallel resources for the computations are presented in the case of the forced simulation-times.
