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RESEARCH PAPERS: Forced Convection

An Efficient Localized Radial Basis Function Meshless Method for Fluid Flow and Conjugate Heat Transfer

[+] Author and Article Information
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 32816-2450kassab@mail.ucf.edu

J. Heat Transfer 129(2), 124-136 (May 25, 2006) (13 pages) doi:10.1115/1.2402181 History: Received September 08, 2005; Revised May 25, 2006

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.

Copyright © 2007 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

CHT problem: external convective heat transfer coupled to heat conduction within the solid

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Figure 2

Typical point collocation of data centers

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Figure 3

Collocation topology for internal, boundary, and corner data centers

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Figure 4

Problem domain and typical decomposition

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Figure 5

Iteration process averaging across an interface

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Figure 6

FVM mesh and point collocation of cavity

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Figure 7

FVM and meshless velocity contours

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Figure 8

FVM and meshless x velocity profiles at x=0, 0.25, 0.5, 0.75, and 1.0m

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Figure 9

FVM and meshless velocity vectors and magnitude contours for the lid-driven cavity

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Figure 10

FVM and meshless temperature contours for the lid-driven cavity

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Figure 11

FVM and meshless x velocity component at vertical center line

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Figure 12

FVM and meshless y velocity component at horizontal center line

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Figure 13

Geometry and properties for parallel plates

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Figure 14

FVM and meshless velocity contours

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Figure 15

FVM and meshless temperature contours

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Figure 16

FVM and meshless temperature profiles at 1∕4, 1∕2, 3∕4, and 1∕1 channel length

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Figure 17

FVM and meshless heat flux along interface

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Figure 18

Geometry and properties for square obstruction

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Figure 19

Velocity contours: (a) FVM, and (b) meshless

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Figure 20

FVM and meshless x velocity profiles at x=7, 8, 9, 10, and 11cm

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Figure 21

FVM and meshless ∂u∕∂y after the obstruction

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Figure 22

FVM and meshless temperature contours

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Figure 23

Zoomed in FVM and meshless obstruction temperature contours in the square obstruction

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Figure 24

Data center distribution and FVM mesh for cooling plenum, cooling hole (2cm width), and main cooling channel:(a) meshless collocation (13,345 data centers) 2cm cooling hole width and (b) finite volume mesh (14,859 finite volumes)

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Figure 25

Comparison of temperature distributions predicted by: (a) meshless and (b) FVM as well as (c) temperature profiles on top region at x=0.15, 0.2, 0.25, 0.3, 0.35, 0.4m and (d) heat flux along top wall of stainless-steel block (y=0.15m) after cooling hole

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Figure 26

Contours of velocity magnitude and velocity profiles: (a) LMRBF velocity contors; (b) FVM velocity contours; and (c) velocity profiles across the channel region at discrete locations x=0.15, 0.2, 0.25, 0.3, 0.35, and 0.4m

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Figure 27

FVM grid and meshless point distribution around the cylinder

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Figure 28

FVM and meshless velocity magnitude contours around the cylinder

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Figure 29

Pressure coefficient around the cylinder

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Figure 30

Viscous stress coefficient around the cylinder

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