// // $(this).bind('click', function() { ShowTwo(url)}); // } // }); // } // //获取下载pdf注册的cookie // function getcookie() { // var cookieName = "pdfddcookie"; // var cookieValue = null; //返回cookie的value值 // if (document.cookie != null && document.cookie != '') { // var cookies = document.cookie.split(';'); //将获得的所有cookie切割成数组 // for (var i = 0; i < cookies.length; i++) { // var cookie = cookies[i]; //得到某下标的cookies数组 // if (cookie.substring(0, cookieName.length + 2).trim() == cookieName.trim() + "=") {//如果存在该cookie的话就将cookie的值拿出来 // cookieValue = cookie.substring(cookieName.length + 2, cookie.length); // break // } // } // } // if (cookieValue != "" && cookieValue != null) {//如果存在指定的cookie值 // return false; // } // else { // // return true; // } // } // function ShowTwo(webUrl){ // alert("22"); // $.funkyUI({url:webUrl,css:{width:"600",height:"500"}}); // } //window.onload = pdfdownloadjudge;
JAMP> Vol.3 No.9, September 2015
Share This Article:
Cite This Paper >>

A New Iterative Method for Multi-Moving Boundary Problems Based Boundary Integral Method

Abstract Full-Text HTML XML Download Download as PDF (Size:621KB) PP. 1126-1137
DOI: 10.4236/jamp.2015.39140    2,111 Downloads   2,529 Views   Citations
Author(s)    Leave a comment
Kawther K. Al-Swat, Said G. Ahmed*

Affiliation(s)

Department of Mathematics and Statistics, Faculty of Science, Taif University, Taif, Kingdom of Saudi Arabia.

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.

KEYWORDS

Multi-Moving Boundary Problems, Vaporization Problem, Ablation Problem, Source and Sink Method, Finite Element Method, Heat Balance Integral Method, Boundary Integral Method

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.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] Meaad, N.M.I. (2014) Mesh-Less Methods and Its Application to Free and Moving Boundary Problems. M.Sc. Thesis, Zagazig University, Zagazig. Supervision S. G. Ahmed.
[2] Crank, J. (1984) Free and Moving Boundary Problems. Clarendon Press, Oxford.
[3] Mohamd, N.A.E. (2002) Boundary Elements Methods and Its Non-Linear Analysis of Hydrofoils. Supervisors: Prof. S. G. Ahmed and Prof. A. F. Abd-Elgawad. Zagazig University, Zagazig.
[4] Nofal, T.A. and Ahmed, S.G. (2015) An Integral Method to Solve Phase-Change Problems with/without Mushy Zones. Journal of Applied Mathematics and Mathematics, II, 152-157.
[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.
[7] Zerroukat, M. and Chatwin, C.R. (1994) Computational Moving and Boundary Problems. Research Studies Press Ltd., Baldock.
[8] Ruan, Y. and Zabaras, N. (1991) An Inverse Finite Element Technique to Determine The change of Phase Interface Location in Two-Dimensional Melting Problem. Communications in Applied Numerical Methods, 7, 325-338.
http://dx.doi.org/10.1002/cnm.1630070411
[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.
[10] Liu, W., Chen, Y., Jun, S., Chen, J.-S., Belytschko, T., Pan, C., Uras, R. and Chang, C. (1996) Overview and Application of the Reproducing Kernel Particle Methods. Archive of Computational Methods in Engineering: State of the Art Reviews, 3, 3-80.
http://dx.doi.org/10.1007/BF02736130
[11] Ahmed, S.G. (2005) A New Algorithm for Moving Boundary Problems Subject to Periodic Boundary Conditions. International Journal of Numerical Methods for Heat and Fluid Flow, 16, 18-27.
[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.
[14] Mehdi, A. and Hsieh, C.K. (1994) Solution of Ablation and Combination of Ablation and Stefan Problems by a Source and Sink Method. Numerical Heat Transfer, Part A, 26, 67-86.
http://dx.doi.org/10.1080/10407789408955981
[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.

  
comments powered by Disqus
JAMP Subscription
E-Mail Alert
JAMP Most popular papers
Publication Ethics & OA Statement
JAMP News
Frequently Asked Questions
Recommend to Peers
Recommend to Library
Contact Us

Copyright © 2020 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.