High-order alternating direction implicit method based on compact integrated-RBF approximations for unsteady/steady convection-diffusion equations

Thai-Quang, N. and Mai-Duy, N. and Tran, C.-D. and Tran-Cong, T. (2012) High-order alternating direction implicit method based on compact integrated-RBF approximations for unsteady/steady convection-diffusion equations. CMES: Computer Modeling in Engineering and Sciences, 89 (3). pp. 189-220. ISSN 1526-1492

Abstract

In this paper, the alternating direction implicit (ADI) method reported in [You (2006)] for the convection-diffusion equation is implemented in the context of compact integrated radial basis function (CIRBF) approximations. The CIRBF approximations are constructed over 3-point stencils, where extra information is incorporated via two forms: only nodal second-order derivative values (Scheme 1), and both nodal first- and second-order derivative values (Scheme 2). The resultant algebraic systems are sparse, especially for Scheme 2 (tridiagonal matrices). Several steady and non-steady problems are considered to verify the present schemes and to compare their accuracy with some other ADI schemes. Numerical results show that highly accurate results are obtained with the proposed methods.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Copyright © 2012 Tech Science Press.
Faculty / Department / School: Historic - Faculty of Engineering and Surveying - Department of Mechanical and Mechatronic Engineering
Date Deposited: 10 Apr 2013 01:52
Last Modified: 19 Aug 2014 02:58
Uncontrolled Keywords: alternating direction implicit (ADI); compact integrated-RBF stencils; convection-diffusion equation; high-order approximations
Fields of Research : 01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010302 Numerical Solution of Differential and Integral Equations
01 Mathematical Sciences > 0102 Applied Mathematics > 010201 Approximation Theory and Asymptotic Methods
09 Engineering > 0913 Mechanical Engineering > 091307 Numerical Modelling and Mechanical Characterisation
Socio-Economic Objective: E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
Identification Number or DOI: 10.3970/cmes.2012.089.189
URI: http://eprints.usq.edu.au/id/eprint/23045

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