An efficient localized radial basis function meshless method for fluid flow and conjugate heat transfer

    Authors

    E. Divo;A. J. Kassab

    Comments

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    Abbreviated Journal Title

    J. Heat Transf.-Trans. ASME

    Keywords

    PARTIAL-DIFFERENTIAL-EQUATIONS; DATA APPROXIMATION SCHEME; NAVIER-STOKES; EQUATIONS; SCATTERED DATA; DOMAIN DECOMPOSITION; INCOMPRESSIBLE-FLOW; ELEMENT METHOD; DYNAMICS; MULTIQUADRICS; SURFACE; Thermodynamics; Engineering, Mechanical

    Abstract

    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.

    Journal Title

    Journal of Heat Transfer-Transactions of the Asme

    Volume

    129

    Issue/Number

    2

    Publication Date

    1-1-2007

    Document Type

    Article; Proceedings Paper

    Language

    English

    First Page

    124

    Last Page

    136

    WOS Identifier

    WOS:000244535000004

    ISSN

    0022-1481

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