A new high-order time-kernel BIEM for the Burgers equation

Mai-Duy, N. and Tran-Cong, T. and Tanner, R. I. (2006) A new high-order time-kernel BIEM for the Burgers equation. CMES: Computer Modeling in Engineering and Sciences, 16 (3). pp. 177-186. ISSN 1526-1492

Abstract

This paper presents a new high-order time-kernel boundary-integral-equation method (BIEM) for numerically solving transient problems governed by the Burgers equation. Instead of using high-order Lagrange polynomials such as quadratic and quartic interpolation functions, the proposed method employs integrated radial-basis-function networks (IRBFNs) to represent the unknown functions in boundary and volume integrals. Numerical implementations of ordinary and double integrals involving time in the presence of IRBFNs are discussed in detail. The proposed method is verified through the solution of diffusion and convection-diffusion problems. A comparison of the present results and those obtained by low-order BIEMs and other methods is also given.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: No replies to 2 requests for copyright clearance, so made live 22/7/2008.
Depositing User: Dr Nam Mai-Duy
Faculty / Department / School: Historic - Faculty of Engineering and Surveying - Department of Mechanical and Mechatronic Engineering
Date Deposited: 11 Oct 2007 00:56
Last Modified: 02 Jul 2013 22:42
Uncontrolled Keywords: Burgers equation; radial-basis-function networks; transient problems; time-dependent fundamental solutions; boundary-integral-equation methods
Fields of Research (FOR2008): 01 Mathematical Sciences > 0101 Pure Mathematics > 010109 Ordinary Differential Equations, Difference Equations and Dynamical Systems
08 Information and Computing Sciences > 0801 Artificial Intelligence and Image Processing > 080110 Simulation and Modelling
09 Engineering > 0913 Mechanical Engineering > 091307 Numerical Modelling and Mechanical Characterisation
Socio-Economic Objective (SEO2008): E Expanding Knowledge > 97 Expanding Knowledge > 970109 Expanding Knowledge in Engineering
Identification Number or DOI: doi: 10.3970/cmes.2006.016.177
URI: http://eprints.usq.edu.au/id/eprint/2080

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