On the formulation of hyperbolic Stefan problems
Authors:
A. D. Solomon, V. Alexiades, D. G. Wilson and J. Drake
Journal:
Quart. Appl. Math. 43 (1985), 295-304
MSC:
Primary 80A20; Secondary 35R35
DOI:
https://doi.org/10.1090/qam/814228
MathSciNet review:
814228
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Abstract: The study of phase change processes governed by hyperbolic heat transfer is at an embryonic stage. We raise here some of the relevant questions and make some remarks on the formulation and qualitative behavior of hyperbolic Stefan problems. In particular, we correct an error in the interface condition appearing in two earlier studies, and present an explicit solution to a simple one-phase problem and study its behavior. Finally we describe an enthalpy (weak) formulation for a two-phase problem and report on a few numerical experiments based on it.
M. Sadd and J. Didlake, Non-fourier melting of a semi-infinite solid, Jornal of Heat Transfer, 25–28 (1977)
- L. M. De Socio and G. Gualtieri, A hyperbolic Stefan problem, Quart. Appl. Math. 41 (1983/84), no. 2, 253–259. MR 719509, DOI https://doi.org/10.1090/S0033-569X-1983-0719509-0
- A. D. Solomon, D. G. Wilson, and V. Alexiades, Explicit solutions to phase change problems, Quart. Appl. Math. 41 (1983/84), no. 2, 237–243. MR 719507, DOI https://doi.org/10.1090/S0033-569X-1983-0719507-5
- Murray H. Protter and Hans F. Weinberger, Maximum principles in differential equations, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1967. MR 0219861
- R. Courant and D. Hilbert, Methods of mathematical physics. Vol. I, Interscience Publishers, Inc., New York, N.Y., 1953. MR 0065391
- Philip M. Morse and Herman Feshbach, Methods of theoretical physics. 2 volumes, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1953. MR 0059774
D. Bogy and P. Naghdi, On heat conduction and wave propagation in rigid solids, Journal of Mathematical Physics 11, 917–923 (1970)
A. Solomon, Numerical methods for solving Stefan-type problems, Res Mechanica, to appear
- Alan Solomon, Some remarks on the Stefan problem, Math. Comp. 20 (1966), 347–360. MR 202391, DOI https://doi.org/10.1090/S0025-5718-1966-0202391-1
- Lloyd N. Trefethen, Group velocity in finite difference schemes, SIAM Rev. 24 (1982), no. 2, 113–136. MR 652463, DOI https://doi.org/10.1137/1024038
M. Sadd and J. Didlake, Non-fourier melting of a semi-infinite solid, Jornal of Heat Transfer, 25–28 (1977)
L. DeSocio and G. Gualtieri, A Hyperbolic Stefan Problem Quarterly of Applied Mathematics 41, 253–259 (1983)
A. Solomon, V. Alexiades and D. Wilson, Explicit solutions to phase change problems, Quarterly of Applied Mathematics 41, 237–243 (1983)
M. Protter and H. Weinberger, Maximum principles in differential equations, Prentice Hall, Englewood Cliffs, 1967
R. Courant and D. Hilbert, Methods of mathematical physics, Vol. II, Interscience, New York, 1962
P. Morse and H. Feshbach, Methods of theoretical physics, Pt. I, McGraw Hill, New York, 1953, p. 865
D. Bogy and P. Naghdi, On heat conduction and wave propagation in rigid solids, Journal of Mathematical Physics 11, 917–923 (1970)
A. Solomon, Numerical methods for solving Stefan-type problems, Res Mechanica, to appear
A. Solomon, Some remarks on the Stefan problem, Mathematics of Computation 20, 347–360 (1966)
L. Trefethen, Group velocity in finite difference schemes, SIAM Review 24, 113–136 (1982)
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Article copyright:
© Copyright 1985
American Mathematical Society
