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| Multi-Dimentional Upwind Schemes for the Euler Equations on Unstructured Grids
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International Journal of Engineering (IJE) |
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Table of Contents |
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Volume: 3 Issue: 2 |
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Pages: 85-219 |
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Publication
Date: April 2009 |
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ISSN
(Online): 1985-2312 |
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185 - 200 |
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Author(s) |
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Published
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18-05-2009 |
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Publisher |
CSC
Journals, Kuala Lumpur,
Malaysia |
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ADDITIONAL
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| Keywords Abstract References Cited by Related Articles Collaborative
Colleague |
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KEYWORDS: CFD, Euler equation, Unstructured triangular meshes, Upwind, Fluctuation, Roe |
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| In the last few years, upwind methods have become very popular in the modeling of advection dominated flows and in particular those which contain strong discontinuities. For more than a decade, these methods have been used successfully to solve numerically the one-dimensional Euler equations [10]. Fluctuation distribution has been recently [3] introduced as an alternative to conventional upwinding. In contrast to standard upwinding the fluctuation distribution approach extends naturally to multidimensional flow without requiring any splitting along coordinate directions.
The technique uses a narrow-stencil, local, piecewise linear reconstruction of the flow field solution. The flow field is updated in time by propagating a subset of eigenmodes of the convective operator. Different choices of the eigenmode subset lead to different fluctuation distribution schemes [8].
In this paper the presented models of fluctuation distribution for the Euler equations have reached the stage where they can be used reliably to achieve maximal computational efficiency to practical steady state problems in aerodynamics (Supersonic oblique shock reflection, Flow in a channel with a Bump, Symmetric Constricted channel flows, flow around NACA 0012 aerofoil, flows in a turbine-blade cascade VKI LS-59 ).
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| 1 |
PL. Roe. “Approximate Riemann solvers, parameter vectors and difference schemes”. J. Computational Physics. 43(2):357-372, 1981.
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| 2 |
H. Deconinck, R. Struijs, G. Bourgois, PL. Roe. “High resolution shock capturing cell vertex advection schemes for unstructured grids”. Lecture series, Van Kareman Institute for fluid dynamics. 5: H1-H79,1994.
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| 3 |
PL. Roe. “Approximate Riemann solvers, parameter vectors and difference schemes”. J. Computational Physics. 43(2):357-372, 1981.
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H. Deconinck, R. Struijs, G. Bourgois, PL. Roe. “High resolution shock capturing cell vertex advection schemes for unstructured grids”. Lecture series, Van Kareman Institute for fluid dynamics. 5: H1-H79,1994.
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| 5 |
H. Deconinck, R. Struijs, G. Bourgois, H. Paillere, PL. Roe. “Multidimensional upwind methods for unstructured grids. In AGARD, Special Course on Unstructured Grid Methods for Advection Dominated Flows. N92-27671 18-34, 1992.
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H. Deconinck, PL., Roe, R. Struijs. “A multidimensional generalization of roe’s flux difference splitter for the Euler equations”. Journal of Computers Fluids. 22:215-222, 1993.
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| 7 |
R. Struijs, H. Deconinck, P. De Palma, PL. Roe, KG. Powell. “Progress on multidimensional upwind Euler solvers for unstructured grids”. In Computational Fluid Dynamics Conference, 10th, Honolulu, HI, June 24-26, 1991.
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| 8 |
H. Paillere, H. Deconinck, E. Van der Weide. “Upwind residual distribution methods for compressible flow”. In 28th CFD Lecture Series, Bruxelles, VKI for Fluid Dynamics, 1997.
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| 9 |
PL. Roe. “Discrete models for the numerical analysis of time-dependent multidimensional gas dynamics”. Journal of Computational Physics, 43:458-476, 1986.
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| 10 |
PL. Roe. “Algorithmic trends in CFD, chapter Beyond the Riemann Problem”. Springer-Verlag, Part I, 341-367, 1993.
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| 11 |
D. Sidilkover, PL. Roe. “Unifaction of some advection schemes in two dimensions”. Technical report, ICASE, TR-95-10, 1995.
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| 12 |
ME. Hubbard. “Multidimensional Upwinding and grid adaptation for conservation Laws”. PhD Thesis, University of Reading, 1996.
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| 13 |
L. Mesaros. “Multi-Dimensional Fluctuation Schemes for the Euler Equations on Unstructured Grids”. PhD Thesis, University of Michigan,1995.
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| 14 |
N. Venkatakrishnan. “A Perspective on Unstructured Grid Flow Solvers”. ICASE Report 95-3, 1995.
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| 15 |
13. PL. Roe, L. Mesaros. “An improved wave model for the multi-dimensional upwinding of the Euler equations”. In Proceedings of the Thirteenth International Conference on Numerical Methods in Fluid Dynamics, Rome, July 1992.
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| 16 |
P. De Palma, H. Deconinck and R. Struijs. “Investigation of Roe’s 2D wave decomposition models for the Euler equations”. Technical report, Von Karman Institute for Fluid Dynamics, TN-172, June 1990.
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B. Laskarzewska and M. Mehrvar. “Atmospheric Chemistry in Existing Air Atmospheric Dispersion Models and Their Applications: Trends, Advances and Future in Urban Areas in Ontario, Canada and in Other Areas of the World”. International Journal of Engineering (IJE), Volume (3) : Issue (1), 2009.
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R. Atan, A. A. A. Ghani, M. Selamat and R. Mahmod.“Automating Measurement for Software Process Models using Attribute Grammar Rules”. International Journal of Engineering (IJE), Volume (1) : Issue (2), 2007.
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S. Manchanda, M. Dave and S. B. Singh. “Genetic Information System Development and Maintenance Model For Effective Software Maintenance and Reuse”. International Journal of Engineering (IJE), Volume (1) : Issue (1), 2007.
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Université Hadj Lakhdar, Batna
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docin
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| Mounir Aksas : Colleagues
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| Abdelmouman H. Benmachiche : Colleagues
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