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Javierre, E. (author), Vuik, C. (author), Vermolen, F.J. (author), van der Zwaag, S. (author)In this paper we present a critical comparison of the suitability of several numerical methods, level set, moving grid and phase eld model, to address two well known Stefan problems in phase transformation studies: melting of a pure phase and diusional solid state phase transformations in a binary system. Similarity solutions are applied to...report 2005
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Vermolen, F.J. (author), Vuik, C. (author)A general model for the dissolution of particles in multi-component alloys is proposed and analyzed. The model is based on diffusion equations with cross-terms for the several species, combined with a Stefan condition as the equation of motion of the interface between the particle and diffusant phase. To facilitate the analysis we use a...report 2003
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Vermolen, F.J. (author), Vuik, C. (author), Van der Zwaag, S. (author)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...report 2002
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Vermolen, F.J. (author), Vuik, C. (author), Segal, A. (author)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...report 2002
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Vermolen, F.J. (author), Vuik, C. (author), Van der Zwaag, S. (author)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...report 2001
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Vermolen, F.J. (author), Vuik, C. (author), van der Zwaag, S. (author)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...report 2001
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Vermolen, F.J. (author), Vuik, C. (author)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...report 2001
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- Vermolen, F. (author), Vuik, K. (author), Van der Zwaag, S. (author) conference paper 1997
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