Numerical Solution for Two-Sided Stefan Problem
Keyword(s):
In this paper, we consider a two-phase Stefan problem in one-dimensional space for parabolic heat equation with non-homogenous Dirichlet boundary condition. This problem contains a free boundary depending on time. Therefore, the shape of the problem is changing with time. To overcome this issue, we use a simple transformation to convert the free-boundary problem to a fixed-boundary problem. However, this transformation yields a complex and nonlinear parabolic equation. The resulting equation is solved by the finite difference method with Crank-Nicolson scheme which is unconditionally stable and second-order of accuracy in space and time. The numerical results show an excellent accuracy and stable solutions for two test examples.
1988 ◽
Vol 73
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pp. 104-118
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2007 ◽
Vol 8
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pp. 959-979
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2018 ◽
Vol 43
(7)
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pp. 1073-1101
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2014 ◽
Vol 25
(01)
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pp. 165-194
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1984 ◽
Vol 24
(2)
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pp. 243-267
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