A time discretization scheme based on integrated radial basis functions for heat transfer and fluid flow problems

Le, T. T. V. and Mai-Duy, N. and Le-Cao, K. and Tran-Cong, T. (2018) A time discretization scheme based on integrated radial basis functions for heat transfer and fluid flow problems. Numerical Heat Transfer Part B: Fundamentals, 74 (2). pp. 498-518. ISSN 1040-7790

Abstract

This paper reports a new numerical procedure, which is based on integrated radial basis functions (IRBFs) and Cartesian grids, for solving time-dependent differential problems that can be defined on non-rectangular domains. For space discretisations, compact five-point IRBF stencils [Journal of Computational Physics, vol. 235, pp. 302-321, 2013] are utilised. For time discretisations, a two-point IRBF scheme is proposed, where the time derivative is approximated in terms of not only nodal function values at the current and previous time levels but also nodal derivative values at the previous time level. This allows functions other than a linear one to also be captured well on a time step. The use of the RBF width as an additional parameter to enhance the approximation quality with respect to time is also explored. Various kinds of test problems of heat transfer and fluid flows are conducted to demonstrate attractiveness of the present compact approximations.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Accepted version embargoed until 1 September 2019 (12 months), in accordance with the copyright policy of the publisher.
Faculty/School / Institute/Centre: Current - Faculty of Health, Engineering and Sciences - School of Mechanical and Electrical Engineering
Date Deposited: 11 Feb 2019 02:31
Last Modified: 13 Jun 2019 02:16
Uncontrolled Keywords: time discretisations; integrated radial basis functions; compact approximations; heat transfer and fluid flows
Fields of Research : 01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010302 Numerical Solution of Differential and Integral Equations
Socio-Economic Objective: E Expanding Knowledge > 97 Expanding Knowledge > 970109 Expanding Knowledge in Engineering
Identification Number or DOI: 10.1080/10407790.2018.1515329
URI: http://eprints.usq.edu.au/id/eprint/35479

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