Diffuse interface models of solidification with convection: The choice of a finite interface thickness
Institute for Digital Materials Science, Karlsruhe University of Applied Sciences, Moltkestraße 30, 76133 Karlsruhe, Germany
2 Physikalisch-Astronomische Fakultät, Friedrich-Schiller-Universität-Jena, 07743 Jena, Germany
3 Department of Theoretical and Mathematical Physics, Laboratory of Multi-Scale Mathematical Modeling, Ural Federal University, Lenin ave., 51, Ekaterinburg 620000, Russia
4 Interdisciplinary Centre for Advanced Materials Simulation, Ruhr-Universität Bochum, Universitätsstrasse 150, 44780 Bochum, Germany
a e-mail: email@example.com
Received in final form: 28 June 2019
Published online: 11 February 2020
The thin interface limit aims at minimizing the effects arising from a numerical interface thickness, inherent in diffuse interface models of solidification and microstructure evolution such as the phase field model. While the original formulation of this problem is restricted to transport by diffusion, we consider here the case of melt convection. Using an analysis of the coupled phase field-fluid dynamic equations, we show here that such a thin interface limit does also exist if transport contains both diffusion and convection. This prediction is tested by comparing simulation studies, which make use of the thin-interface condition, with an analytic sharp-interface theory for dendritic tip growth under convection.
© The Author(s) 2020
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Open access funding provided by Projekt DEAL.