A time discretization scheme based on integrated radial basis functions for heat transfer and fluid flow problems. (3rd August 2018)

• Record Type: Journal Article
• Authors: Le, T. T. V.; Mai-Duy, N.; Le-Cao, K.; Tran-Cong, T.
• Is Part Of: Numerical heat transfer. Volume 74:Number 2(2018)
• Page Start: 498
• Page End: 518
• Publication Date: 2018-08-03
• Subjects: Heat -- Transmission -- Measurement -- Periodicals; Mass transfer -- Measurement -- Periodicals; Numerical analysis -- Periodicals; Heat -- Transmission -- Periodicals; Mass transfer -- Periodicals; 621.4022
• DOI: 10.1080/10407790.2018.1515329
• Languages: English
• ISSNs: 1040-7790

Abstract

Abstract: This article 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 discretizations, compact five-point IRBF stencils are utilized. For time discretizations, 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 the the attractiveness of the present compact approximations.