Modellierung und zuverlässige Simulation von allgemeinen Mehrkomponenten-Reaktions- und Transportprozessen in poroesen Medien
Modelling and efficient and reliable simulation of reactive transport in porous media plays a major role, in particular concerning the fate of contaminants in soils and aquifers. We present a comprehensive model taking saturated-unsaturated fluid flow and homogeneous and heterogeneous reactions for multiple components, both in quasi-static equilibrium and in kinetic non-equilibrium, into account. In this way ariving at a highly nonlinear time-dependent problem in several varables, at least in three spatial dimensions a reduction in complexity is desired. Therefore various transformation techniques are presentd with the aim to decouple the problem as far as possible. The remaining nonlinear system is approximated with Newton's method using the multigrid method for the arising linear subproblems. As spatial discretization hybridized mixed finite elements for the flow problem and higher order stabilized conformal finite elements are chosen due to their advantageous qualitative properties. In particular we confirm the possibility of qualitatively wrong answers concerning the propagation of contaminant plumes in the context of natural attenuation, if using low order elements or nonadapted grids. As we have to deal with global nonlinear problems, local nonlinear problems have to be solved in the process of static condensation. Large gradients and small reaction zones require grid adaptation based on a posteriori error indicators. In the time discretization the stiffness of the system has to be taken into account, e.g. by appropriate multistep methods.