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High-order Alternating Direction Implicit Method Based on Compact Integrated-RBF Approximations for Unsteady/Steady Convection-Diffusion Equations

N. Thai-Quang1, N. Mai-Duy1, C.-D Tran1, T. Tran-Cong1
Computational Engineering and Science Research Centre, Faculty of Engineering and Surveying, The University of Southern Queensland, Toowoomba, Queensland 4350, Australia.

Computer Modeling in Engineering & Sciences 2012, 89(3), 189-220. https://doi.org/10.3970/cmes.2012.089.189

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.

Keywords

compact integrated-RBF stencils, high-order approximations, alternating direction implicit (ADI), convection-diffusion equation.

Cite This Article

Thai-Quang, N., Mai-Duy, N., Tran, C., 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 & Sciences, 89(3), 189–220.



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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