A Numerical Method for Solving the Inverse Stefan Problem in two Space Variables

1983 ◽  
pp. 57-63 ◽  
Author(s):  
David Colton ◽  
Rembert Reemtsen
Keyword(s):  
Numerical Method ◽  
Stefan Problem

A Numerical Method for a Stefan Problem

AIAA Journal ◽  
1968 ◽  
Vol 6 (9) ◽  
pp. 1821-1822 ◽  
Author(s):  
HAROLD J. BREAUX
Keyword(s):  
Numerical Method ◽  
Stefan Problem

scholarly journals A Numerical Method for the Solution of the Two-Phase Fractional Lamé–Clapeyron–Stefan Problem

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2157
Author(s):  
Marek Błasik
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Analytical Solution ◽  
Numerical Method ◽  
Stefan Problem ◽  
Moving Boundary ◽  
Second Phase ◽  
Time Step ◽  
Partial Differential ◽  
Two Phase

In this paper, we present a numerical solution of a two-phase fractional Stefan problem with time derivative described in the Caputo sense. In the proposed algorithm, we use a special case of front-fixing method supplemented by the iterative procedure, which allows us to determine the position of the moving boundary. The presented method is an extension of a front-fixing method for the one-phase problem to the two-phase case. The novelty of the method is a new discretization of the partial differential equation dedicated to the second phase, which is carried out by introducing a new spatial variable immobilizing the moving boundary. Then, the partial differential equation is transformed to an equivalent integro-differential equation, which is discretized on a homogeneous mesh of nodes with a constant spatial and time step. A new convergence criterion is also proposed in the iterative algorithm determining the location of the moving boundary. The motivation for the development of the method is that the analytical solution of the considered problem is impossible to calculate in some cases, as can be seen in the figures in the paper. Moreover, the change of the boundary conditions makes obtaining a closed analytical solution very problematic. Therefore, creating new numerical methods is very valuable. In the final part, we also present some examples illustrating the comparison of the analytical solution with the results received by the proposed numerical method.

ON STEFAN PROBLEM WITH PRESCRIBED CONVECTION

1994 ◽  
Vol 14 (2) ◽  
pp. 153-166
Author(s):  
Yi Fahuak ◽  
Qiu Yipin
Keyword(s):  
Stefan Problem

Numerical Method for Hetero-Cavities Natural Frequencies’ Determination

2016 ◽  
Vol 10 (3) ◽  
pp. 141
Author(s):  
Fethi Maiz ◽  
Ridha Chouikh ◽  
Amenallah Guizani
Keyword(s):  
Numerical Method ◽  
Natural Frequencies
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