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A global method for coupling transport with chemistry in heterogeneous porous media. (English) Zbl 1425.76231
Summary: Modeling reactive transport in porous media, using a local chemical equilibrium assumption, leads to a system of advection-diffusion PDEs 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 one 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.

MSC:
76S05 Flows in porous media; filtration; seepage
76V05 Reaction effects in flows
76M25 Other numerical methods (fluid mechanics) (MSC2010)
35Q35 PDEs in connection with fluid mechanics
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