scholarly journals The Numerical Solution of an Inverse Two-Phase Stefan Problem

Author(s):  
Tingting Li ◽  
He Yin ◽  
Quangang Wen
Author(s):  
V.I. Vasilyev ◽  
M.V. Vasilyeva ◽  
S.P. Stepanov ◽  
N.I. Sidnyaev ◽  
O.I. Matveeva ◽  
...  

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


1985 ◽  
Vol 8 (1-2) ◽  
pp. 55-82 ◽  
Author(s):  
Irena Pawlow ◽  
Yuji Shindo ◽  
Yoshiyuki Sakawa

2020 ◽  
Vol 20 (2) ◽  
pp. 437-458 ◽  
Author(s):  
Félix del Teso ◽  
Jørgen Endal ◽  
Juan Luis Vázquez

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.


2021 ◽  
Vol 1809 (1) ◽  
pp. 012002
Author(s):  
N G Burago ◽  
A I Fedyushkin

2021 ◽  
Vol 9 (5) ◽  
pp. 486
Author(s):  
Tobias Martin ◽  
Hans Bihs

During the operation of moored, floating devices in the renewable energy sector, the tight coupling between the mooring system and floater motion results in snap load conditions. Before snap events occur, the mooring line is typically slack. Here, the mechanism of energy propagation changes from axial to bending dominant, and the correct modelling of the rotational deformation of the lines becomes important. In this paper, a new numerical solution for modelling the mooring dynamics that includes bending and shearing effects is proposed for this purpose. The approach is based on a geometrically exact beam model and quaternion representations for the rotational deformations. Further, the model is coupled to a two-phase numerical wave tank to simulate the motion of a moored, floating offshore wind platform in waves. A good agreement between the proposed numerical model and reference solutions was found. The influence of the bending stiffness on the motion of the structure was studied subsequently. We found that increased stiffness increased the amplitudes of the heave and surge motion, whereas the motion frequencies were less altered.


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