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A New High-order Time-kernel BIEM for the Burgers Equation

N. Mai-Duy1,2, T. Tran-Cong2, R.I. Tanner3
Corresponding author: Telephone +61 7 4631 1324, Fax +61 74631 2526, E-mail maiduy@usq.edu.au
Faculty of Engineering and Surveying, The University of Southern Queensland, QLD 4350, Australia
School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, NSW 2006, Australia

Computer Modeling in Engineering & Sciences 2006, 16(3), 177-186. https://doi.org/10.3970/cmes.2006.016.177

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.

Keywords

Burgers equation, Radial-basis-function networks, Transient problems, Time-dependent fundamental solutions, Boundary-integral-equation methods.

Cite This Article

Mai-Duy, N., Tran-Cong, T., Tanner, R. (2006). A New High-order Time-kernel BIEM for the Burgers Equation. CMES-Computer Modeling in Engineering & Sciences, 16(3), 177–186.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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