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 JAMP  Vol.3 No.9 , September 2015
A New Iterative Method for Multi-Moving Boundary Problems Based Boundary Integral Method
Abstract: The present paper deals with very important practical problems of wide range of applications. The main target of the present paper is to track all moving boundaries that appear throughout the whole process when dealing with multi-moving boundary problems continuously with time up to the end of the process with high accuracy and minimum number of iterations. A new numerical iterative scheme based the boundary integral equation method is developed to track the moving boundaries as well as compute all unknowns in the problem. Three practical applications, one for vaporization and two for ablation were solved and their results were compared with finite element, heat balance integral and the source and sink results and a good agreement were obtained.
Cite this paper: Al-Swat, K. and Ahmed, S. (2015) A New Iterative Method for Multi-Moving Boundary Problems Based Boundary Integral Method. Journal of Applied Mathematics and Physics, 3, 1126-1137. doi: 10.4236/jamp.2015.39140.
References

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[5]   Ahmed, S.G. and Mekey, M.L. (2010) A Collocation and Cartesian Grid Methods Using New Radial Basis Function to Solve Class of Partial Differential Equations. International Journal of Computer Mathematics, 87, 1349-1362.

[6]   Meshrif, S.A. and Ahmed, S.G. (2007) Approximate Integral Method Applied to Ablation Problem in a Finite Slab. International Symposium on Recent Advances in Mathematics and Its Applications (ISRAMA 2007), Culcutta, 15-17 December 2007, 1-12.

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[9]   Mohamed, W.A. (2012) Advanced Mathematical Analysis for Phase Change Problems with and without Mushy Zones. Supervisors: Prof. S. G. Ahmed and Prof. M. E. Mohamed. Zagazig University, Zagazig.

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[12]   Abd-El Fatah, W.M. and Ahmed, S.G. (2006) Boundary Integral Formulation for Binary Alloys from a Cooling Solid Wall. International Journal of Computational and Applied Mathematics, 5, 687-696.

[13]   Ahmed, S.G. (2003) A New Algorithm for Front Tracking of Ablation Problem in Unbounded Domain. Ain Shams University, Egypt.

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[15]   Ahmed, S.G. (2003) A Numerical Solution for Nonlinear Heat Flow Problem Using Boundary Integral Method. 6th International Conference of Computer Methods and Experimental Measurements for Surface Treatment, Crete, March 2003.

 
 
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