ADI method based on C2-continuous two-node integrated-RBF elements for viscous flows

An-Vo, D.-A. and Mai-Duy, N. and 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, 37 (7). pp. 5184-5203. ISSN 0307-904X

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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.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: © 2012 Elsevier Inc. Permanent restricted access to published version due to publisher copyright policy.
Faculty / Department / School: Historic - Faculty of Engineering and Surveying - Department of Mechanical and Mechatronic Engineering
Date Deposited: 22 Feb 2014 06:45
Last Modified: 11 Nov 2015 02:34
Uncontrolled Keywords: Navier-Stokes equations; integrated-radial-basis-function elements; C2-continuous solutions; Cartesian grid; ADI method; local RBF approximation
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 > 970109 Expanding Knowledge in Engineering
E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
Identification Number or DOI: 10.1016/j.apm.2012.10.034
URI: http://eprints.usq.edu.au/id/eprint/24557

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