van Tl Tycho Noorden

Crystal precipitation and dissolution in a thin strip

We present a two-dimensional micro-scale model for crystal dissolution and precipitation in a porous medium. The local geometry of the pore is represented as a thin strip and the model allows for changes in the pore volume. A formal limiting argument, for the limit of the width of the strip going to zero, leads to a system of one-dimensional effective upscaled equations. We show that the effective equations allow for travelling-wave solutions and prove the existence and uniqueness of these. Numerical solutions of the effective equations are compared with numerical solutions of the original equations on the thin strip and with analytical results. We also show that a model from the literature that does not allow changes in the pore volume can be obtained from the present model as a formal limit.

Homogenisation of a locally periodic medium with areas of low and high diffusivity

We aim at understanding transport in porous materials consisting of regions with both high and low diffusivities. We apply a formal homogenisation procedure to the case where the heterogeneities are not arranged in a strictly periodic manner. The result is a two-scale model formulated in x-dependent Bochner spaces. We prove the weak solvability of the limit two-scale model for a prototypical advection–diffusion system of minimal size. A special feature of our analysis is that most of the basic estimates (positivity,

Effective Dispersion Equations for Reactive Flows Involving Free Boundaries at the Microscale

L^\infty

A Broyden Rank p +1 Update Continuation Method with Subspace Iteration

-bounds, uniqueness, energy inequality) are obtained in

Corrector estimates for the homogenization of a locally periodic medium with areas of low and high diffusivity

x

An upscaled model for biofilm growth in a thin strip

-dependent Bochner spaces.

A Stefan problem modelling crystal dissolution and precipitation

We consider a pore-scale model for reactive flow in a thin two-dimensional strip, where the convective transport dominates the diffusion. Reactions take place at the lateral boundaries of the strip (the walls), where the reaction product can deposit in a layer with a nonnegligible thickness compared to the width of the strip. This leads to a free boundary problem, in which the moving interface between the fluid and the deposited (solid) layer is explicitly taken into account. Using asymptotic expansion methods, we derive an upscaled, one-dimensional model by averaging in the transversal direction. The result is consistent with (Taylor dispersion) models obtained previously for a constant geometry. Finally, numerical computations are presented to compare the outcome of the effective (upscaled) model with the transversally averaged, two-dimensional solution.

The efficient computation of periodic states of cyclically operated chemical processes

In this paper we present an efficient branch-following procedure that can be used not only to compute branches of periodic solutions of periodically forced dynamical systems but also to determine the stability of the periodic solutions. The procedure combines Broydens method with a subspace iteration method to determine the dominant eigenvalues. The method has connections with the hybrid Newton--Picard methods developed by Lust et al. in [SIAM J. Sci. Comput., 19 (1998) pp. 1188--1209]. A convergence analysis of the procedure is presented. The method is applied to the computation of periodic states of a reverse flow reactor, and its performance is compared with two variants of the hybrid Newton--Picard method.

Crystal dissolution and precipitation in porous media :

We prove an upper bound for the convergence rate of the homogenization limit epsilon -> 0 for a linear transmission problem for a advection-diffusion(-reaction) system posed in areas with low an ...