Searched for: subject%3A%22similarity%255C+solutions%22
(1 - 11 of 11)
document
Giacomelli, Lorenzo (author), Gnann, M.V. (author), Peschka, Dirk (author)
We consider the thin-film equation for a class of free boundary conditions modelling friction at the contact line, as introduced by E and Ren. Our analysis focuses on formal long-time asymptotics of solutions in the perfect wetting regime. In particular, through the analysis of quasi-self-similar solutions, we characterize the profile and the...
journal article 2023
document
Vural, Asya (author)
The porous medium equation $\dv{t}u=\dv{x}(k(u)\dv{x}u)$ is a non-linear degenerate parabolic partial differential equation. Consequently, existence and uniqueness of its solutions is not immediately evident.<br/>This bachelor thesis presents a detailed discussion of Atkinson's and Peletier's 1971 article ``Similarity profiles of flows through...
bachelor thesis 2021
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Vermolen, F.J. (author)
In this paper the Zener theory on precipitate growth in supersaturated alloys for planar, cylindrical and spherical geometries is extended to multi-component alloys. The obtained solutions can be used to check the results from numerical simulations under simplified conditions. Further, the multi-component solutions are used to derive the quasi...
report 2006
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Javierre, E. (author), Vuik, C. (author), Vermolen, F.J. (author), Segal, A. (author)
A mathematical model is proposed for the dissolution of stoichiometric particles in binary alloys occurring during the heat treatments of as-cast aluminium alloys prior to hot extrusion. The Level Set method is used to capture the interface location implicitly. The front velocity, only dened on the moving interface, should be advected to the...
report 2005
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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), 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), Zitha, P.L.J. (author), Bruining, J. (author)
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....
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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Snel, H. (author)
A model is derived for the calculation of the properties of a jet exhausting into a non-uniform main flow, at an arbitrary angle to the initial jet direction. The model is a generalisation of an earlier jet-ina-main flow model for uniform main flows. Semi empirical input is limited to an entrainment relation and a relation for form factors of...
report 1975
Searched for: subject%3A%22similarity%255C+solutions%22
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