Efficient and Accurate Simulation of Large General Reactive Multicomponent Transport Processes in Porous Media by Model-Preserving a priori and a posteriori Decoupling Techniques
of Large General Reactive Multicomponent Transport Processes in
Porous Media by Model-Preserving a priori and a posteriori
Decoupling Techniques
Creators: name: Knabner, Peter
name: Kraeutle, Serge
name: Prechtel, Alexander
name: Knabner, Peter
Publisher: name: XVI International Conference on Computational Methods in Water Resources
Year: 2006

description: Detailed modelling of reactive transport processes in the
underground often requires the consideration of a wide range of
reactive species. A prominent example is natural attenuation, that
is the assessment and monitoring of microbially catalysed
degradation processes of organic contaminants in the subsoil or
aquifer with full geochemistry. Often the reactions
exhibit a wide range of relaxation times, which advises to model
those reactions being much faster than the time scale of the
transport processes in a quasistationary manner, e.g. as
(algebraicly described) equilibrium processes. Additionally not
only mobile species (in solution) appear, but also immobile ones
(attached to the porous skeleton). In summary, the resulting
system is not semilinear and parabolic, but rather quasilinear and
couples partial differential equations (pde), ordinary
differential equations and algebraic equations. An often used
approach is operator splitting, in which transport and reaction
becomes (iteratively) decoupled. This procedure either introduces
a further consistency error (in the non-interative version) which
can only be controlled by the time stepping, or applies a fixed
point type iteration of unclear convergence properties. We rather
propose, after appropriate (mixed) finite element discretization,
to deal with the full discrete nonlinear system (the
 Global Implicit Approach,in principal by a damped
Newton's method). To make the problem still feasible we advise two
means: The first is concerned with the continuous model and aims
at a transformation of the dependent variables such that as many
as possible are determined by decoupled linear pde's or by local
algebraic relations, leading to a smaller coupled system. The
problem lies here in the combined appearance of kinetics and
equilibrium and mobile and immobile species. Alternatively to this
exact a priori decoupling we use an a posteriori decoupling on the
level of the linear system of equation in the Newton's method by sparsening, i.e.
ignoring weak couplings in the Jacobian matrix. The resulting
benefit in the solution of the linear system should supersede a
possible deterioration in the convergence of the iterative method,
being now only an approximate Newtons's method. Iterative operator splitting can
be viewed as of this type with two half-steps, first ignoring e.g. the reactive
couplings (the transport step) and then ignoring the transport couplings (the
reaction step). The introduced larger flexibility of the method helps to find
selective couplings where there is still a good (Newton-like) convergence in cases
where operator splitting fails. The benefit of the two approaches, which in principle
are also combinable, will be elucidated for several large problems from the
hydrological literature.