A localized radial basis function (RBF) meshless method is developed for coupled viscous fluid flow and convective heat transfer problems. The method is based on new localized radial-basis function (RBF) expansions using Hardy Multiquadrics for the sought-after unknowns. An efficient set of formulae are derived to compute the RBF interpolation in terms of vector products thus providing a substantial computational savings over traditional meshless methods. Moreover, the approach developed in this paper is applicable to explicit or implicit time marching schemes as well as steady-state iterative methods. We apply the method to viscous fluid flow and conjugate heat transfer (CHT) modeling. The incompressible Navier–Stokes are time marched using a Helmholtz potential decomposition for the velocity field. When CHT is considered, the same RBF expansion is used to solve the heat conduction problem in the solid regions enforcing temperature and heat flux continuity of the solid/fluid interfaces. The computation is accelerated by distributing the load over several processors via a domain decomposition along with an interface interpolation tailored to pass information through each of the domain interfaces to ensure conservation of field variables and derivatives. Numerical results are presented for several cases including channel flow, flow in a channel with a square step obstruction, and a jet flow into a square cavity. Results are compared with commercial computational fluid dynamics code predictions. The proposed localized meshless method approach is shown to produce accurate results while requiring a much-reduced effort in problem preparation in comparison to other traditional numerical methods.
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Research Papers
An Efficient Localized Radial Basis Function Meshless Method for Fluid Flow and Conjugate Heat Transfer
Eduardo Divo,
Eduardo Divo
Department of Engineering Technology,
University of Central Florida
, Orlando, FL 32816-2450
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Alain J. Kassab
Alain J. Kassab
Department of Mechanical, Materials, and Aerospace Engineering,
e-mail: kassab@mail.ucf.edu
University of Central Florida
, Orlando, FL 32816-2450
Search for other works by this author on:
Eduardo Divo
Department of Engineering Technology,
University of Central Florida
, Orlando, FL 32816-2450
Alain J. Kassab
Department of Mechanical, Materials, and Aerospace Engineering,
University of Central Florida
, Orlando, FL 32816-2450e-mail: kassab@mail.ucf.edu
J. Heat Transfer. Feb 2007, 129(2): 124-136 (13 pages)
Published Online: May 25, 2006
Article history
Received:
September 8, 2005
Revised:
May 25, 2006
Citation
Divo, E., and Kassab, A. J. (May 25, 2006). "An Efficient Localized Radial Basis Function Meshless Method for Fluid Flow and Conjugate Heat Transfer." ASME. J. Heat Transfer. February 2007; 129(2): 124–136. https://doi.org/10.1115/1.2402181
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