A mathematical and numerical model for reactive fluid flow systems

We formulate mathematical and numerical models for multispecies, multi-phase and non-isothermal reactive fluid flow in porous media focusing on the chemical reactions and the transport of solutes. Mass conservation and stability in the 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 kappa = 1/3 related schemes to approximate the advective flux and the central difference scheme for the diffusive flux. On non-rectangular grids we recommend the VF9 scheme for the estimation of the diffusive flux. Our model exists as a code.