A high-order upwind control-volume method based on integrated RBFs for fluid-flow problems

Mai-Duy, N. and Tran-Cong, T. (2011) A high-order upwind control-volume method based on integrated RBFs for fluid-flow problems. International Journal for Numerical Methods in Fluids, 67 (12). pp. 1973-1992. ISSN 0271-2091

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Abstract

This paper is concerned with the development of a high-order upwind conservative discretization method for the simulation of flows of a Newtonian fluid in two dimensions. The fluid-flow domain is discretized using a Cartesian grid from which non-overlapping rectangular control volumes are formed. Line integrals arising from the integration of the diffusion and convection terms over control volumes are evaluated using the middle-point rule. One-dimensional integrated radial basis function schemes using the multiquadric basis function are employed to represent the variations of the field variables along the grid lines. The convection term is effectively treated using an upwind scheme with the deferred-correction strategy. Several highly non-linear test problems governed by the Burgers and the Navier–Stokes equations are simulated, which show that the proposed technique is stable, accurate and converges well.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Accepted version deposited in accordance with the copyright policy of the publisher.
Depositing User: Dr Nam Mai-Duy
Faculty / Department / School: Historic - Faculty of Engineering and Surveying - Department of Mechanical and Mechatronic Engineering
Date Deposited: 19 Jan 2012 23:09
Last Modified: 03 Jul 2013 00:57
Uncontrolled Keywords: integrated RBF; Cartesian grid; control volume; upwind scheme; deferred-correction technique; high-order approximation
Fields of Research (FOR2008): 08 Information and Computing Sciences > 0802 Computation Theory and Mathematics > 080202 Applied Discrete Mathematics
09 Engineering > 0915 Interdisciplinary Engineering > 091501 Computational Fluid Dynamics
09 Engineering > 0913 Mechanical Engineering > 091307 Numerical Modelling and Mechanical Characterisation
Socio-Economic Objective (SEO2008): 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: doi: 10.1002/fld.2477
URI: http://eprints.usq.edu.au/id/eprint/20392

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