Garcke, Harald and Stinner, Bjorn (2006) Second order phase field asymptotics for multi-component systems. INTERFACES AND FREE BOUNDARIES, 8 (2). pp. 131-157. ISSN 1463-9971,
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We derive a phase field model which approximates a sharp interface model for solidification of a multicomponent alloy to second order in the interfacial thickness epsilon. Since in numerical computations for phase field models the spatial grid size has to be smaller than epsilon the new approach allows for considerably more accurate phase field computations than have been possible so far. In the classical approach of matched asymptotic expansions the equations to lowest order in epsilon lead to the sharp interface problem. Considering the equations to the next order, a correction problem is derived. It turns out that, when taking a possibly non-constant correction term to a kinetic coefficient in the phase field model into account, the correction problem becomes trivial and the approximation of the sharp interface problem is of second order in epsilon. By numerical experiments, the better approximation property is well supported. The computational effort to obtain an error smaller than a given value is investigated, revealing an enormous efficiency gain.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | SHARP INTERFACE LIMITS; UNEQUAL CONDUCTIVITIES; MODEL; SOLIDIFICATION; ALLOYS; CONVERGENCE; EVOLUTION; phase field models; sharp interface models; numerical simulations; matched asymptotic expansions |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Harald Garcke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 02 Mar 2021 08:36 |
| Last Modified: | 02 Mar 2021 08:36 |
| URI: | https://pred.uni-regensburg.de/id/eprint/35178 |
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