Nonsmooth Analysis and Free Boundary Problems for Potential Flow

1995 ◽  
pp. 275-295
Author(s):  
Srdjan Stojanovic
Keyword(s):  
Free Boundary ◽  
Potential Flow ◽  
Nonsmooth Analysis ◽  
Free Boundary Problems ◽  
Boundary Problems

scholarly journals Numerical solution of free-boundary problems in fluid mechanics. Part 3. Bubble deformation in an axisymmetric straining flow

1984 ◽  
Vol 148 ◽  
pp. 37-43 ◽  
Author(s):  
G. Ryskin ◽  
L. G. Leal
Keyword(s):  
Free Boundary ◽  
Potential Flow ◽  
Free Boundary Problems ◽  
Early Stage ◽  
Extensional Flow ◽  
Reynolds Numbers ◽  
Boundary Problems ◽  
Bubble Deformation ◽  
Real Flow ◽  
Uniaxial Extensional Flow

We consider the deformation of a bubble in a uniaxial extensional flow for Reynolds numbers in the range 0.1 [les ] R [les ] 100. The computations show that the bubble bursts at a relatively early stage of deformation for R [ges ] O(10), never reaching the highly elongated shapes observed and predicted at lower Reynolds numbers. We also compute the deformation of the bubble under the assumption of potential flow, and conclude that the potential-flow solution provides a good approximation to the real flow in this case for R [ges ] O(100).

scholarly journals On optimal regularity of free boundary problems and a conjecture of De Giorgi

2005 ◽  
Vol 58 (8) ◽  
pp. 1051-1076 ◽  
Author(s):  
Herbert Koch ◽  
Giovanni Leoni ◽  
Massimiliano Morini
Keyword(s):  
Free Boundary ◽  
Free Boundary Problems ◽  
Optimal Regularity ◽  
Boundary Problems

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.

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