Crystal dissolution and precipitation in porous media : L1L^1-contraction and uniqueness

In this note we continue the analysis of the pore-scale model for crystal dissolution and precipitation in porous media proposed in [C. J. van Duijn and I. S. Pop, Crystal dissolution and precipitation in porous media: pore scale analysis, J. Reine Angew. Math. 577 (2004), 171–211]. There the existence of weak solutions was shown. We prove an L1-contraction property of the pore-scale model. As a direct consequence we obtain the uniqueness of (weak) solutions

Convergence analysis of mixed numerical schemes for reactive in a porous medium

This paper deals with the numerical analysis of an upscaled model describing the reactive flow in a porous medium. The solutes are transported by advection and diffusion and undergo precipitation and dissolution. The reaction term and, in particular, the dissolution term has a particular, multi-valued character, which leads to stiff dissolution fronts. We consider the Euler implicit method for the temporal discretization and the mixed finite element for the discretization in time. More precisely, we use the lowest order Raviart-Thomas elements. As an intermediate step we consider also a semi-discrete mixed variational formulation (continuous in space). We analyse the numerical schemes and prove the convergence to the continuous formulation. Apart from the proof for the convergence, this also yields an existence proof for the solution of the model in mixed variational formulation. Numerical experiments are performed to study the convergence behavior