Effects of direction decoupling in flux calculation in finite volume solvers

Smith, M. R., Macrossan, Michael N. and Abdel-Jawad, Madhat (2008) Effects of direction decoupling in flux calculation in finite volume solvers. Journal of Computational Physics, 227 8: 4142-4161. doi:10.1016/j.jcp.2007.12.015

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Author Smith, M. R.
Macrossan, Michael N.
Abdel-Jawad, Madhat
Title Effects of direction decoupling in flux calculation in finite volume solvers
Journal name Journal of Computational Physics   Check publisher's open access policy
ISSN 0021-9991
Publication date 2008-04-01
Year available 2007
Sub-type Article (original research)
DOI 10.1016/j.jcp.2007.12.015
Open Access Status File (Author Post-print)
Volume 227
Issue 8
Start page 4142
End page 4161
Total pages 20
Place of publication New York
Publisher Academic Press
Language eng
Subject 240502 Fluid Physics
Abstract In a finite volume CFD method for unsteady flow, fluxes of mass, momentum and energy are exchanged between cells over a series of small time steps. The conventional approach, which we will refer to as direction decoupling, is to estimate fluxes across interfaces in a regular array of cells by using a one-dimensional flux expression based on the component of flow velocity normal to the interface between cells. This means that fluxes cannot be exchanged between diagonally adjacent cells since they share no cell interface, even if the local flow conditions dictate that the fluxes should flow diagonally. The direction decoupling imposed by the numerical method requires that the fluxes reach a diagonally adjacent cell in two time-steps. In order to evaluate the e®ects of this direction decoupling, we examine two numerical methods which differ only in that one uses direction decoupling while the other does not. We examine a generalized form of Pullin's Equilibrium Flux Method (EFM) [J. Comput. Physics, v34, 1980, pp 231-244] which we have called the True Direction Equilibrium Flux Method (TDEFM). The TDEFM fluxes, derived from kinetic theory, flow not only between cells sharing an interface, but ultimately to any cell in the grid. TDEFM is used here to simulate a blast wave and an imploding flow problem on a structured rectangular mesh and is compared with results from direction decoupled EFM. Since both EFM and TDEFM are identical in the low CFL number limit, differences between the results demonstrate the detrimental e®ect of direction decoupling. Differences resulting from direction decoupling are also shown in the simulation of hypersonic flow over a rectangular body. The computational cost of allowing the EFM fluxes to flow in the correct directions on the grid is minimal.
Keyword Computational Fluid Dynamics
Kinetic Theory of Gases
Direct simulation
Euler solver
Flux direction
particle fluxes
Q-Index Code C1
Q-Index Status Provisional Code
Additional Notes Available online 31 December 2007

Document type: Journal Article
Sub-type: Article (original research)
Collections: Excellence in Research Australia (ERA) - Collection
School of Mechanical & Mining Engineering Publications
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Citation counts: TR Web of Science Citation Count  Cited 13 times in Thomson Reuters Web of Science Article | Citations
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Created: Thu, 20 Dec 2007, 09:41:41 EST by Michael N Macrossan on behalf of School of Mechanical and Mining Engineering