A numerical scheme based on compact integrated-RBFs and Adams-Bashforth/Crank-Nicolson algorithms for diffusion and unsteady fluid flow problems

Thai-Quang, N. and Le-Cao, K. and Mai-Duy, N. and Tran, C.-D. and Tran-Cong, T. (2013) A numerical scheme based on compact integrated-RBFs and Adams-Bashforth/Crank-Nicolson algorithms for diffusion and unsteady fluid flow problems. Engineering Analysis with Boundary Elements , 37 (12). pp. 1653-1667. ISSN 0955-7997

Abstract

This paper presents a high-order approximation scheme based on compact integrated radial basis function (CIRBF) stencils and second-order Adams-Bashforth/Crank-Nicolson algorithms for solving time-dependent problems in one and two space dimensions. We employ CIRBF stencils, where the RBF approximations are locally constructed through integration and expressed in terms of nodal values of the function and its derivatives, to discretise the spatial derivatives in the governing equation. We adopt the Adams-Bashforth and Crank-Nicolson algorithms, which are second-order accurate, to discretise the temporal derivatives. The performance of the proposed scheme is investigated numerically through the solution of several test problems, including heat transfer governed by the diffusion equation, shock wave propagation and shock-like solution governed by the Burgers' equation, and torsionally oscillating lid-driven cavity flow governed by the Navier-Stokes equation in the primitive variables. Numerical experiments show that the proposed scheme is stable and high-order accurate in reference to the exact solution of analytic test problems and achieves a good agreement with published results for other test problems.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: © 2013 Elsevier Ltd. Published version deposited in accordance with the copyright policy of the publisher.
Faculty / Department / School: Current - Faculty of Health, Engineering and Sciences - School of Mechanical and Electrical Engineering
Date Deposited: 11 Nov 2013 23:33
Last Modified: 11 Nov 2015 02:29
Uncontrolled Keywords: compact integrated-RBF stencils; high-order approximations; time-dependent problems
Fields of Research : 09 Engineering > 0915 Interdisciplinary Engineering > 091501 Computational Fluid Dynamics
01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010399 Numerical and Computational Mathematics not elsewhere classified
01 Mathematical Sciences > 0102 Applied Mathematics > 010201 Approximation Theory and Asymptotic Methods
Socio-Economic Objective: E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
Identification Number or DOI: 10.1016/j.enganabound.2013.09.011
URI: http://eprints.usq.edu.au/id/eprint/24250

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