scholarly journals The Solution of Two-Phase Inverse Stefan Problem Based on a Hybrid Method with Optimization

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Yang Yu ◽  
Xiaochuan Luo ◽  
Haijuan Cui
Keyword(s):  
Conjugate Gradient Method ◽  
Stefan Problem ◽  
Hybrid Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Simulation Experiment ◽  
Adomian Decomposition Method ◽  
Optimization Method ◽  
Two Phase ◽  
Adomian Decomposition

The two-phase Stefan problem is widely used in industrial field. This paper focuses on solving the two-phase inverse Stefan problem when the interface moving is unknown, which is more realistic from the practical point of view. With the help of optimization method, the paper presents a hybrid method which combines the homotopy perturbation method with the improved Adomian decomposition method to solve this problem. Simulation experiment demonstrates the validity of this method. Optimization method plays a very important role in this paper, so we propose a modified spectral DY conjugate gradient method. And the convergence of this method is given. Simulation experiment illustrates the effectiveness of this modified spectral DY conjugate gradient method.

scholarly journals Approximate Analytic Solutions for the Two-Phase Stefan Problem Using the Adomian Decomposition Method

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Xiao-Ying Qin ◽  
Yue-Xing Duan ◽  
Mao-Ren Yin
Keyword(s):  
Stefan Problem ◽  
Decomposition Method ◽  
Moving Boundary ◽  
Adomian Decomposition Method ◽  
Solidification Process ◽  
Analytic Solutions ◽  
Unknown Boundary ◽  
Two Phase ◽  
Metal Solidification ◽  
Adomian Decomposition

An Adomian decomposition method (ADM) is applied to solve a two-phase Stefan problem that describes the pure metal solidification process. In contrast to traditional analytical methods, ADM avoids complex mathematical derivations and does not require coordinate transformation for elimination of the unknown moving boundary. Based on polynomial approximations for some known and unknown boundary functions, approximate analytic solutions for the model with undetermined coefficients are obtained using ADM. Substitution of these expressions into other equations and boundary conditions of the model generates some function identities with the undetermined coefficients. By determining these coefficients, approximate analytic solutions for the model are obtained. A concrete example of the solution shows that this method can easily be implemented in MATLAB and has a fast convergence rate. This is an efficient method for finding approximate analytic solutions for the Stefan and the inverse Stefan problems.

Sign in / Sign up

Export Citation Format

Share Document