Optimal control of the free boundary in a two-phase Stefan problem

2007 ◽  
Vol 223 (2) ◽  
pp. 657-684 ◽  
Author(s):  
Michael Hinze ◽  
Stefan Ziegenbalg
Keyword(s):  
Optimal Control ◽  
Free Boundary ◽  
Stefan Problem ◽  
Two Phase

scholarly journals On the Two-phase Fractional Stefan Problem

2020 ◽  
Vol 20 (2) ◽  
pp. 437-458 ◽  
Author(s):  
Félix del Teso ◽  
Jørgen Endal ◽  
Juan Luis Vázquez
Keyword(s):  
Free Boundary ◽  
Stefan Problem ◽  
Free Boundary Problems ◽  
Classical Problem ◽  
Nonlocal Diffusion ◽  
Two Phase ◽  
Boundary Problems ◽  
Numerical Studies ◽  
The One ◽  
Evolution Type

AbstractThe classical Stefan problem is one of the most studied free boundary problems of evolution type. Recently, there has been interest in treating the corresponding free boundary problem with nonlocal diffusion. We start the paper by reviewing the main properties of the classical problem that are of interest to us. Then we introduce the fractional Stefan problem and develop the basic theory. After that we center our attention on selfsimilar solutions, their properties and consequences. We first discuss the results of the one-phase fractional Stefan problem, which have recently been studied by the authors. Finally, we address the theory of the two-phase fractional Stefan problem, which contains the main original contributions of this paper. Rigorous numerical studies support our results and claims.

Control of the free boundary in a two-phase Stefan problem with flow driven by convection

PAMM ◽  
2007 ◽  
Vol 7 (1) ◽  
pp. 4140027-4140028
Author(s):  
Michael Hinze ◽  
Stefan Ziegenbalg
Keyword(s):  
Free Boundary ◽  
Stefan Problem ◽  
Two Phase

A two phase stefan problem: regularity of the free boundary

1971 ◽  
Vol 88 (1) ◽  
pp. 217-228 ◽  
Author(s):  
J. R. Cannon ◽  
M. Primicerio
Keyword(s):  
Free Boundary ◽  
Stefan Problem ◽  
Two Phase

scholarly journals Numerical Solution for Two-Sided Stefan Problem

2020 ◽  
pp. 444-452
Author(s):  
M.S. Hussein ◽  
Zahraa Adil
Keyword(s):  
Free Boundary ◽  
Boundary Problem ◽  
Stefan Problem ◽  
Dirichlet Boundary ◽  
Dimensional Space ◽  
Two Phase ◽  
Order Of Accuracy ◽  
One Dimensional ◽  
Nonlinear Parabolic ◽  
Nicolson Scheme

     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.

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