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Abstract

The two-dimensional one phase Stefan problem is solved with the method of lines (in alternating directions) using an implicit scheme for time discretization. The resulting boundary value problems for ordinary differential equations are solved by multiple shooting. The algorithm is applied to the problem of continuous casting of steel.

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Literatur

  1. MEYER, G. H.: An alternating direction method for multi-dimensional parabolic free surface problems. Int. J. Num. Meth. Eng. 11 (1977), 741–752.

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  2. MEYER, G. H.: On a free interface problem for linear ordinary differential equations and the one-phase Stefan problem. Num. Math. 16 (1970), 248–267.

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  3. MEYER, G. H.: The numerical solution of Stefan problems with front tracking and smoothing methods. Appl. Math. Comp. 4 (1978), 283–306.

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© 1982 Springer Basel AG

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Brokate, M. (1982). Numerische Lösung eines Zweidimensionalen Freien Randwertproblems. In: Albrecht, J., Collatz, L., Hoffmann, KH. (eds) Numerical Treatment of Free Boundary Value Problems / Numerische Behandlung freier Randwertaufgaben. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 58. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6563-0_2

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  • DOI: https://doi.org/10.1007/978-3-0348-6563-0_2

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-6565-4

  • Online ISBN: 978-3-0348-6563-0

  • eBook Packages: Springer Book Archive

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