Mixed methods for reactive flows involving precipitation-dissolution processes

We consider appropriate numerical methods for the reactive multiphase flow models in a porous medium.  The model has two components: flow and transport. The flow is modeled by Darcy law. The chemical species undergo advection due to underlying flow field and the molecular diffusion and dispersion. In addition, the chemical species are involved in the precipitation-dissolution processes at the porous solid matrix. Even in the case of a one phase and one component flow and transport, the reaction rate description for the dissolution processes is non-Lipschitz leading to a very low regularity of the solution. We will study rigorous convergence of the numerical schemes for this case. In the case of multiphase multicomponent flow and transport processes, we present a domain decomposition based multiscale method.

This work has been done in collaboration with Ben Ganis (Austin), Gergina Pencheva (Austin), Sorin Pop (Eindhoven), Florin Radu (Bergen), Mary Wheeler (Austin), and Ivan Yotov (Pittsburgh).