Pressure-Based Finite-Volume Methods in Computational Fluid Dynamics

[+] Author and Article Information
S. Acharya, B. R. Baliga, K. Karki, J. Y. Murthy, C. Prakash, S. P. Vanka

Department of Mechanical Engineering,  Louisiana State University, Baton Rouge, LA 70803Department of Mechanical Engineering,  McGill University, Montreal, Quebec, Canada H3A 2K6 Innovative Research Inc., 3025 Harbor Lane, Suite 300, Plymouth, MN 55447School of Mechanical Engineering,  Purdue University, West Lafayette, IN 47907 GE Aircraft Engines, 30 Merchant St., Princeton Hill P20, Cincinnati, OH 45246Department of Mechanical Science and Engineering,  University of Illinois, Urbana-Champaign, Urbana IL 61801

J. Heat Transfer 129(4), 407-424 (Jan 07, 2007) (18 pages) doi:10.1115/1.2716419 History: Received December 31, 2006; Revised January 07, 2007

Pressure-based finite-volume techniques have emerged as the methods of choice for a wide variety of industrial applications involving incompressible fluid flow. In this paper, we trace the evolution of this class of solution techniques. We review the basics of the finite-volume method, and trace its extension to unstructured meshes through the use of cell-based and control-volume finite-element schemes. A critical component of the solution of incompressible flows is the issue of pressure-velocity storage and coupling. The development of staggered-mesh schemes and segregated solution techniques such as the SIMPLE algorithm are reviewed. Co-located storage schemes, which seek to replace staggered-mesh approaches, are presented. Coupled multigrid schemes, which promise to replace segregated-solution approaches, are discussed. Extensions of pressure-based techniques to compressible flows are presented. Finally, the shortcomings of existing techniques and directions for future research are discussed.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 1

Control volume around P and associated nomenclature

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Figure 2

Staggered grid arrangement (a) control-volume for scalars and pressure, (b) control-volume for u, and (c) control-volume for v

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Figure 3

Comparison of SIMPLER , SIMPLEC , and PISO for turbulent flow in a sudden expansion geometry (from Jang (31))

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Figure 4

Comparison of (a) SIMPLER with Rhie and Chow correction and (b) SIMPLEM for flow in a driven cavity Re=100 (from Moukalled and Acharya (32))

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Figure 5

Nomenclature for co-located storage scheme

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Figure 6

CVFEM discretization of a planar two-dimensional calculation domain

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Figure 7

CVFEM grid and related nomenclature: (a) internal node and (b) boundary node

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Figure 8

(a) Nomenclature for cell-based finite volume scheme and (b) geometry for higher-order interpolation

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Figure 9

Nomenclature for least-squares interpolation to find cell gradients in cell-based finite volume scheme

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Figure 10

Hybrid mesh adapted to velocity magnitude (left), and streamlines (right) for laminar natural convection over a hot cylinder located in a square box

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Figure 11

Nusselt number along (a) cold wall, and (b) hot wall (Rayleigh number=106 and Prandtl number=0.1) (15), and comparison with benchmark solution of Demirdzic (71)



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