A competition-diffusion system approximation to the classical two-phase Stefan problem

2001 ◽  
Vol 18 (2) ◽  
pp. 161-180 ◽  
Author(s):  
Danielle Hilhorst ◽  
Masato Iida ◽  
Masayasu Mimura ◽  
Hirokazu Ninomiya
Keyword(s):  
Stefan Problem ◽  
Diffusion System ◽  
Two Phase ◽  
Competition Diffusion

Spatial segregation limit of a competition–diffusion system

1999 ◽  
Vol 10 (2) ◽  
pp. 97-115 ◽  
Author(s):  
E. N. DANCER ◽  
D. HILHORST ◽  
M. MIMURA ◽  
L. A. PELETIER
Keyword(s):  
Interspecific Competition ◽  
Latent Heat ◽  
Stefan Problem ◽  
Singular Limit ◽  
Spatial Segregation ◽  
Diffusion System ◽  
Competition Diffusion

We consider a competition–diffusion system and study its singular limit as the interspecific competition rate tend to infinity. We prove the convergence to a Stefan problem with zero latent heat.

A reaction–diffusion system approximation to the two-phase Stefan problem

2001 ◽  
Vol 47 (2) ◽  
pp. 801-812 ◽  
Author(s):  
D. Hilhorst ◽  
M. Iida ◽  
M. Mimura ◽  
H. Ninomiya
Keyword(s):  
Stefan Problem ◽  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
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.

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

Numerical Solution of the Two-Phase Stefan Problem in the Enthalpy Formulation with Smoothing the Coefficients

2021 ◽  
pp. 4-23
Author(s):  
V.I. Vasilyev ◽  
M.V. Vasilyeva ◽  
S.P. Stepanov ◽  
N.I. Sidnyaev ◽  
O.I. Matveeva ◽  
...  
Keyword(s):  
Numerical Solution ◽  
Stefan Problem ◽  
Large Diameter ◽  
Discontinuous Coefficients ◽  
Numerical Calculations ◽  
Smooth Functions ◽  
Two Phase ◽  
Time Layer ◽  
Dirac Delta ◽  
Selection Of

To simulate heat transfer processes with phase transitions, the classical enthalpy model of Stefan is used, accompanied by phase transformations of the medium with absorption and release of latent heat of a change in the state of aggregation. The paper introduces a solution to the two-phase Stefan problem for a one-dimensional quasilinear second-order parabolic equation with discontinuous coefficients. A method for smearing the Dirac delta function using the smoothing of discontinuous coefficients by smooth functions is proposed. The method is based on the use of the integral of errors and the Gaussian normal distribution with an automated selection of the value of the interval of their smoothing by the desired function (temperature). The discontinuous coefficients are replaced by bounded smooth temperature functions. For the numerical solution, the finite difference method and the finite element method with an automated selection of the smearing and smoothing parameters for the coefficients at each time layer are used. The results of numerical calculations are compared with the solution of Stefan’s two-phase self-similar problem --- with a mathematical model of the formation of the ice cover of the reservoir. Numerical simulation of the thawing effect of installing additional piles on the existing pile field is carried out. The temperature on the day surface of the base of the structure is set with account for the amplitude of air temperature fluctuations, taken from the data of the Yakutsk meteorological station. The study presents the results of numerical calculations for concrete piles installed in the summer in large-diameter drilled wells using cement-sand mortars with a temperature of 25 °С. The distributions of soil temperature are obtained for different points in time

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