Open Access

ARTICLE

A Direct Forcing Immersed Boundary Method Employed With Compact Integrated RBF Approximations For Heat Transfer and Fluid Flow Problems

N. Thai-Quang¹, N. Mai-Duy¹, C.-D. Tran¹, T. Tran-Cong^1,2

1 Computational Engineering and Science Research Centre, Faculty of Health, Engineering and Sciences, The University of Southern Queensland, Toowoomba, Queensland 4350, Australia.
2 Corresponding author. Email: thanh.tran-cong@usq.edu.au. Tel: +61 7 4631 1332. Fax: +61 7 4631 2110.

Computer Modeling in Engineering & Sciences 2013, 96(1), 49-90. https://doi.org/10.3970/cmes.2013.096.049

Abstract

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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