On the Numerical Treatment of Moving Boundary Problems
| Autor: | Sabine Crusius, John Ågren, Lars Höglund, Ursula Knoop, Gerhard Inden |
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| Rok vydání: | 1992 |
| Předmět: |
Diffusion equation
Mathematics::Operator Algebras Numerical analysis Mathematical analysis Metals and Alloys Stefan problem Finite difference Thermodynamics Condensed Matter Physics Grid Interface position Exact solutions in general relativity Planar Materials Chemistry Physical and Theoretical Chemistry Mathematics |
| Zdroj: | International Journal of Materials Research. 83:673-678 |
| ISSN: | 2195-8556 1862-5282 |
| Popis: | Some numerical methods for solving a Stefan problem are discussed and compared with the exact solution. The growth of a planar particle from a supersaturated solution (or solidification from a supercooled liquid) is considered. It is found that the Murray-Landis method, based on a finite difference technique to solve the diffusion equation on a contracting grid, yields a poor accuracy for high supersaturations. The enthalpy method, also based on the finite difference technique and an interpolation formula for obtaining the interface position, shows a satisfactory performance at high supersaturations but a less satisfactory one at low supersaturations. It is demonstrated that the poor accuracy of the Murray-Landis method depends on the application of a less accurate flux-balance equation for finite time increments and the procedure for displacing the grid points. A modification of the Murray-Landis method is developed and is found to have superior numerical performance. |
| Databáze: | OpenAIRE |
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