We consider a simplified model for vertical non-stationary groundwater flow, which includes dynamic capillary pressure effects. Specifically, we consider a viscous Burgers-type equation that is extended with a third-order term containing mixed derivatives in space and time. We analyse the one-dimensional boundary value problem and investigate numerically its long-time behaviour. The numerical schemes discussed here take into account possible discontinuities

We study the reactive flow through a capillary tube. The solute particles are transported and diffused by the fluid. At the tube lateral boundary they undergo an adsorption–desorption process. The transport and reaction parameters are such that we have large, dominant Pe´clet and Damkohler numbers with respect to the ratio of characteristic transversal and longitudinal lengths. Using the anisotropic singular perturbation technique we derive the

In this note we complete 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, 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.

See http://vacatures.tue.nl/web/Vacature.aspx?VacatureNummer=V32.991&Taal=English

See http://vacatures.tue.nl/web/Vacature.aspx?VacatureNummer=V32.992&Taal=English