A global method for coupling transport with chemistry in heterogeneous porous media. (arXiv:0912.3867v1 [math.NA])

Modeling reactive transport in porous media, using a local chemical
equilibrium assumption, leads to a system of advection-diffusion PDE's coupled
with algebraic equations. When solving this coupled system, the algebraic
equations have to be solved at each grid point for each chemical species and at
each time step. This leads to a coupled non-linear system. In this paper a
global solution approach that enables to keep the software codes for transport
and chemistry distinct is proposed. The method applies the Newton-Krylov
framework to the formulation for reactive transport used in operator splitting.
The method is formulated in terms of total mobile and total fixed
concentrations and uses the chemical solver as a black box, as it only requires
that on be able to solve chemical equilibrium problems (and compute
derivatives), without having to know the solution method. An additional
advantage of the Newton-Krylov method is that the Jacobian is only needed as an
operator in a Jacobian matrix times vector product. The proposed method is
tested on the MoMaS reactive transport benchmark.

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Original source : http://arxiv.org/abs/0912.3867...