The finite cell method for spatially varying dispersions in coupled multispecies reactive transprot problems

Colloidal transport and dynamics in porous media can be well described by multi-species reactive transport equations where the governing equations are coupled by first-order reactions. The solution of this type of coupled equations causes considerable computational effort. Additional difficulty is caused by the spatial inhomogeneity of species in porous media which calls for spatially varying dispersion coefficients. In such a setting, analytic solutions are only available for special cases. In the forthcoming paper, we will firstly present a spatial discretization of the problem by the finite cell method, which is an embedded domain approach using a high order finite element method, where the time domain is discretized by finite differences. We will demonstrate the efficiency and stability of this approach and discuss further advantages. Secondly, we will present different methods to solve the coupled problem where the coupling stems from the reactive terms. Here, we will compare different conventional fixed-point iteration methods with a decoupling scheme utilized for the derivation of analytical solutions. The basic idea is to decompose the multiple reactive species by introducing auxiliary variables. The decoupling scheme can be carried over to our numerical framework, i.e. our in-house code AdhoC, which results in the computational time speedup in the order of one magnitude. We will verify all presented numerical schemes by comparison to analytic solutions or benchmark problems and discuss their efficiency. We will conclude the final paper with a practical application.     «

Colloidal transport and dynamics in porous media can be well described by multi-species reactive transport equations where the governing equations are coupled by first-order reactions. The solution of this type of coupled equations causes considerable computational effort. Additional difficulty is caused by the spatial inhomogeneity of species in porous media which calls for spatially varying dispersion coefficients. In such a setting, analytic solutions are only available for special cases. In...     »