×
Rose, Milton E.

An enthalpy scheme for Stefan problems in several dimensions. (English) Zbl 0787.65094

Appl. Numer. Math. 12, No. 1-3, 229-238 (1993).
This paper is an extension of the author’s one-dimensional enthalpy scheme [J. Sci. Comput. (to appear)] to multi-dimensional Stefan problems. Results from numerical experimentations with two-dimensional geometries are presented.
Reviewer: R.S.Anderssen (Canberra)

Cited in 8 Documents

MSC:

65Z05 Applications to the sciences
35K05 Heat equation
80A22 Stefan problems, phase changes, etc.
35R35 Free boundary problems for PDEs
35Q72 Other PDE from mechanics (MSC2000)

Keywords:

Stefan problems; enthalpy scheme; multi-dimensional Stefan problems; numerical experimentations
Cite Review PDF
Full Text: DOI

References:

[1] Crank, J., Free and Moving Boundary Problems (1984), Oxford University Press: Oxford University Press New York · Zbl 0547.35001
[2] Elliot, C. M., Error analysis of the enthalpy method, IMA J. Numer. Anal., 7, 61-71 (1987) · Zbl 0638.65088
[3] Rose, M. E., A method for calculating solutions of parabolic equations with a free boundary, Math. Comp., 14, 249-256 (1960) · Zbl 0096.10102
[4] Rose, M. E., Compact finite volume schemes for the diffusion equation, J. Sci. Comput., 4, 3 (1989)
[5] M.E. Rose, An implicit enthalpy scheme for one-phase Stefan problems, J. Sci. Comput.; M.E. Rose, An implicit enthalpy scheme for one-phase Stefan problems, J. Sci. Comput. · Zbl 0725.65128
[6] White, R. E., A numerical solution of the enthalpy formulation of the Stefan problem, SIAM J. Numer. Anal., 19, 1129-1157 (1982) · Zbl 0501.65058
[7] White, R. E., A modified finite difference scheme for the Stefan problem, Math. Comp., 41, 164, 337-347 (1983) · Zbl 0533.65079
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.