Mathematical models for particle dissolution in metallic alloys

This paper is a review of a suite of mathematical models of increasing complexity on particle dissolution in metallic alloys. This work deals with models for multi-component particle dissolution in multi-component alloys, where various chemical species diffuse simultaneously, and a two-dimensional model incorporating interfacial reactions as in...

Deflation in preconditioned conjugate gradient methods for Finite Element Problems

We investigate the influence of the value of deflation vectors at interfaces on the rate of convergence of preconditioned conjugate gradient methods applied to a Finite Element discretization for an elliptic equation. Our set-up is a Poisson problem in two dimensions with continuous or discontinuous coefficients that vary in several orders of...

A mathematical model for the dissolution of stoichiometric particles in multi-component alloys

A general model for the dissolution of stoichiometric particles in multi-component alloys is proposed and analysed. We introduce the concept of mass-conserving solutions and give a self-similar solution for the resulting Stefan-problem. Furthermore, we show that particle dissolution in multi-component alloys can under certain circumstances be...

A model for a viscous preflush prior to gelation in a porous medium

In this paper we propose and analyse a simplified mathematical model on the effect of a fully miscible preflush on gel-placement in an oil reservoir. The approach is based on a segregated flow model even if the two phases are fully miscible. For the rate of a constant injection rate condition, fully implicit solutions can be constructed....

Some mathematical aspects of particle dissolution and cross-diffusion in multi-component alloys

A general model for the dissolution of stoichiometric particles, taking into account the influences of cross-diffusion, in multi-component alloys is proposed and analyzed using a diagonalisation argument. We give a self-similar solution for the resulting Stefanproblem and state when the solutions are mass-conserving. We also give criteria for...

The influence of deflation vectors at interfaces on the deflated conjugate gradient method

We investigate the influence of the value of deflation vectors at interfaces on the rate of convergence of preconditioned conjugate gradient methods. Our set-up is a Laplace problem in two dimensions with continuous or discontinuous coeffcients that vary in several orders of magnitude. In the continuous case we are interested in the convergence...

The influence of relative permeability functions on the oil and water production

A numerical method to solve the Buckley-Leverett equation and some applications from petroleum engineering