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A mathematical and numerical model for reactive fluid flow systems. (English) Zbl 0997.76094
Summary: We formulate mathematical and numerical models for multispecies, multi-phase and non-isothermal reactive fluid flow in porous media focusing on chemical reactions and transport of solutes. Mass conservation and stability in time integration are emphasized. We use cell-centered finite volume differencing in space and an implicit Runge-Kutta method in time. Assuming two space dimensions, we introduce flux approximation for arbitrarily shaped convex quadrilaterals. On equidistant and variable sized rectangular grids we choose limited \(k=1/3\) related schemes to approximate advective flux, and the central difference scheme for diffusive flux. On non-rectangular grids we recommend the VF9 scheme for the estimation of diffusive flux. Our model exists as a code.

MSC:
76V05 Reaction effects in flows
76M12 Finite volume methods applied to problems in fluid mechanics
80A32 Chemically reacting flows
76S05 Flows in porous media; filtration; seepage
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