High-order alternating direction implicit method based on compact integrated-RBF approximations for unsteady/steady convection-diffusion equations
Article
Article Title | High-order alternating direction implicit method based on compact integrated-RBF approximations for unsteady/steady convection-diffusion equations |
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ERA Journal ID | 3460 |
Article Category | Article |
Authors | Thai-Quang, N. (Author), Mai-Duy, N. (Author), Tran, C.-D. (Author) and Tran-Cong, T. (Author) |
Journal Title | CMES Computer Modeling in Engineering and Sciences |
Journal Citation | 89 (3), pp. 189-220 |
Number of Pages | 32 |
Year | 2012 |
Place of Publication | United States |
ISSN | 1526-1492 |
1526-1506 | |
Digital Object Identifier (DOI) | https://doi.org/10.3970/cmes.2012.089.189 |
Web Address (URL) | https://www.techscience.com/CMES/v89n3/26882 |
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 | alternating direction implicit (ADI); compact integrated-RBF stencils; convection-diffusion equation; high-order approximations |
ANZSRC Field of Research 2020 | 490303. Numerical solution of differential and integral equations |
490101. Approximation theory and asymptotic methods | |
401706. Numerical modelling and mechanical characterisation | |
Public Notes | Files associated with this item cannot be displayed due to copyright restrictions. |
Byline Affiliations | Computational Engineering and Science Research Centre |
Institution of Origin | University of Southern Queensland |
https://research.usq.edu.au/item/q1wz5/high-order-alternating-direction-implicit-method-based-on-compact-integrated-rbf-approximations-for-unsteady-steady-convection-diffusion-equations
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