ADI method based on C2-continuous two-node integrated-RBF elements for viscous flows
Article
An-Vo, D.-A., Mai-Duy, N., Tran, C.-D. and Tran-Cong, T.. 2013. "ADI method based on C2-continuous two-node integrated-RBF elements for viscous flows." Applied Mathematical Modelling: simulation and computation for engineering and environmental systems. 37 (7), pp. 5184-5203. https://doi.org/10.1016/j.apm.2012.10.034
| Article Title | ADI method based on C2-continuous two-node integrated-RBF elements for viscous flows |
|---|---|
| ERA Journal ID | 48 |
| Article Category | Article |
| Authors | An-Vo, D.-A. (Author), Mai-Duy, N. (Author), Tran, C.-D. (Author) and Tran-Cong, T. (Author) |
| Journal Title | Applied Mathematical Modelling: simulation and computation for engineering and environmental systems |
| Journal Citation | 37 (7), pp. 5184-5203 |
| Number of Pages | 20 |
| Year | 2013 |
| Publisher | Elsevier |
| Place of Publication | United States |
| ISSN | 0307-904X |
| 1872-8480 | |
| Digital Object Identifier (DOI) | https://doi.org/10.1016/j.apm.2012.10.034 |
| Web Address (URL) | https://www.sciencedirect.com/science/article/pii/S0307904X12006397 |
| Abstract | We propose a C2-continuous alternating direction implicit (ADI) method for the solution of the streamfunction-vorticity equations governing steady 2D incompressible viscous fluid flows. Discretisation is simply achieved with Cartesian grids. Local two-node integrated radial basis function elements (IRBFEs) [D.-A. An-Vo, N. Mai-Duy, T. Tran-Cong, A C2-continuous control-volume technique based on Cartesian grids and two-node integrated-RBF elements for second-order elliptic problems, CMES: Computer Modeling in Engineering & Sciences 72 (2011) 299-334] are used for the discretisation of the diffusion terms, and then the convection terms are incorporated into system matrices by treating nodal derivatives as unknowns. ADI procedure is applied for the time integration. Following ADI factorisation, the two-dimensional problem becomes a sequence of one-dimensional problems. The solution strategy consists of multiple use of a one-dimensional sparse matrix algorithm that helps saving the computational cost. High levels of accuracy and efficiency of the present methods are demonstrated with solutions of several benchmark problems defined on rectangular and non-rectangular domains. |
| Keywords | Navier-Stokes equations; integrated-radial-basis-function elements; C2-continuous solutions; Cartesian grid; ADI method; local RBF approximation |
| 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 | File reproduced in accordance with the copyright policy of the publisher/author. |
| Byline Affiliations | Computational Engineering and Science Research Centre |
| Institution of Origin | University of Southern Queensland |
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