A direct forcing immersed boundary method employed with compact integrated RBF approximations for heat transfer and fluid flow problems

Thai-Quang, N. and Mai-Duy, N. and Tran, C.-D. and Tran-Cong, T. (2013) A direct forcing immersed boundary method employed with compact integrated RBF approximations for heat transfer and fluid flow problems. CMES: Computer Modeling in Engineering and Sciences, 96 (1). pp. 49-90. ISSN 1526-1492

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In this paper, we present a numerical scheme, based on
the direct forcing immersed boundary (DFIB) approach and compact integrated radial basis function (CIRBF) approximations, for solving the Navier-Stokes equations in two dimensions. The problem domain of complicated shape is embedded in a Cartesian grid containing Eulerian nodes. Non-slip conditions on the inner boundaries, represented by Lagrangian nodes, are imposed by means of the DFIB method, in which a smoothed version of the discrete delta functions is utilised to transfer the physical quantities between
two types of nodes. The velocities and pressure variables are approximated locally on Eulerian nodes using 3-node CIRBF stencils, where first- and second-order derivative values of the field variables are also included in the RBF approximations. The present DFIB-CIRBF scheme is verified through the solution of several test problems including Taylor-Green vortices, rotational flow, lid-driven cavity
flow with multiple solid bodies, flow between rotating
circular and fixed square cylinders, and natural convection in an eccentric annulus between two circular cylinders. Numerical results obtained using relatively coarse grids are in good agreement with available data in the literature.

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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Copyright © 2013 Tech Science Press. Accepted version deposited in accordance with the copyright policy of the publisher. Permanent restricted access to published version due to publisher copyright policy.
Faculty/School / Institute/Centre: Current - Faculty of Health, Engineering and Sciences - School of Mechanical and Electrical Engineering
Date Deposited: 05 Feb 2014 20:53
Last Modified: 12 Nov 2015 05:45
Uncontrolled Keywords: compact integrated RBF; immersed boundary; direct forcing; viscous flow; heat transfer
Fields of Research : 01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010302 Numerical Solution of Differential and Integral Equations
09 Engineering > 0915 Interdisciplinary Engineering > 091505 Heat and Mass Transfer Operations
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: 10.3970/cmes.2013.096.049
URI: http://eprints.usq.edu.au/id/eprint/24559

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