A compact five-point stencil based on integrated RBFs for 2D second-order differential problems

Mai-Duy, N. and Tran-Cong, T. (2013) A compact five-point stencil based on integrated RBFs for 2D second-order differential problems. Journal of Computational Physics, 235. pp. 302-321. ISSN 0021-9991

Abstract

In this paper, a compact 5-point stencil for the discretisation of second-order partial differential equations (PDEs) in two space dimensions is proposed. We employ integrated radial basis functions in one dimension (1D-IRBFs)to construct the approximations for the dependent variable and its derivatives over the three nodes in each direction of the stencil. Certain nodal values of the second-order derivatives are incorporated into the approximations with help of the integration constants. In the case of elliptic PDEs, one algebraic equation if formed at each interior node, and the obtained final system, of which each row has 5 non-zero entries, is solved iteratively using a Picard scheme. In the case of parabolic PDEs discretised with a Crank Nicolson procedure, a set of three simultaneous algebraic equations is established at each interior node and the three equations through the implicit elimination approach. Linear and non-linear test problems, including lid-driven cavity flow and natural convection between the outer square and in the inner cylinder, are considered to verify the proposed stencil.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: © 2012 Elsevier Inc. Published version restricted in accordance with the copyright policy of the publisher.
Faculty / Department / School: Current - Faculty of Health, Engineering and Sciences - No Department
Date Deposited: 17 Apr 2014 06:12
Last Modified: 09 Mar 2015 04:43
Uncontrolled Keywords: compact local approximations; high-order approximations; elliptic PDEs; parabolic PDEs; integrated radial basis functions
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
Socio-Economic Objective: E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
Identification Number or DOI: 10.1016/j.jcp.2012.10.048
URI: http://eprints.usq.edu.au/id/eprint/24983

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