A Conserving Discretization for the Free Boundary in a Two-Dimensional Stefan Problem

1998 ◽  
Vol 141 (1) ◽  
pp. 1-21 ◽  
Author(s):  
Guus Segal ◽  
Kees Vuik ◽  
Fred Vermolen
Keyword(s):  
Free Boundary ◽  
Stefan Problem ◽  
Two Dimensional

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.

Regularization of a two-dimensional two-phase inverse Stefan problem

1997 ◽  
Vol 13 (3) ◽  
pp. 607-619 ◽  
Author(s):  
D D Ang ◽  
A Pham Ngoc Dinh ◽  
D N Thanh
Keyword(s):  
Stefan Problem ◽  
Two Dimensional ◽  
Two Phase

The Two-dimensional Problem with Free Boundary in Problems of Medicine

2021 ◽  
Author(s):  
Fatimat Kh. Kudayeva ◽  
Aslan Kh. Zhemukhov ◽  
Aslan L. Nagorov ◽  
Arslan A. Kaygermazov ◽  
Diana A. Khashkhozheva ◽  
...  
Keyword(s):  
Free Boundary ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Problem With Free Boundary

scholarly journals Free boundary problems in shock reflection/diffraction and related transonic flow problems

2015 ◽  
Vol 373 (2050) ◽  
pp. 20140276 ◽  
Author(s):  
Gui-Qiang Chen ◽  
Mikhail Feldman
Keyword(s):  
Free Boundary ◽  
High Speed ◽  
Free Boundary Problems ◽  
Fluid Flows ◽  
Shock Reflection ◽  
Two Dimensional ◽  
Open Problems ◽  
Boundary Problems ◽  
Flow Problems ◽  
Concave Corner

Shock waves are steep wavefronts that are fundamental in nature, especially in high-speed fluid flows. When a shock hits an obstacle, or a flying body meets a shock, shock reflection/diffraction phenomena occur. In this paper, we show how several long-standing shock reflection/diffraction problems can be formulated as free boundary problems, discuss some recent progress in developing mathematical ideas, approaches and techniques for solving these problems, and present some further open problems in this direction. In particular, these shock problems include von Neumann's problem for shock reflection–diffraction by two-dimensional wedges with concave corner, Lighthill's problem for shock diffraction by two-dimensional wedges with convex corner, and Prandtl-Meyer's problem for supersonic flow impinging onto solid wedges, which are also fundamental in the mathematical theory of multidimensional conservation laws.

scholarly journals On the pointwise jump condition at the free boundary in the 1-phase Stefan problem

2005 ◽  
Vol 4 (2) ◽  
pp. 357-366
Author(s):  
Donatella Danielli ◽  
◽  
Marianne Korten ◽  
Keyword(s):  
Free Boundary ◽  
Stefan Problem ◽  
Jump Condition
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