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Positivity of flux vector splitting schemes

Gressier, Jérémie and Villedieu, Philippe and Moschetta, Jean-Marc Positivity of flux vector splitting schemes. (1999) Journal of Computational Physics, vol. 1 (n° 1). pp. 199-220. ISSN 0021-9991

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Official URL: http://dx.doi.org/10.1006/jcph.1999.6337

Abstract

Over the last ten years, robustness of schemes has raised an increasing interest among the CFD community. One mathematical aspect of scheme robustness is the positivity preserving property. At high Mach numbers, solving the conservative Euler equations can lead to negative densities or internal energy. Some schemes such as the flux vector splitting (FVS) schemes are known to avoid this drawback. In this study, a general method is detailed to analyze the positivity of FVS schemes. As an application, three classical FVS schemes (Van Leer's, Hänel's variant, and Steger and Warming's) are proved to be positively conservative under a CFL-like condition. Finally, it is proved that for any FVS scheme, there is an intrinsic incompatibility between the desirable property of positivity and the exact resolution of contact discontinuities.

Item Type:Article
Additional Information:Thanks to Springer editor. The definitive version is available at http://www.springerlink.com The original PDF of the article can be found at Journal of Computational Physics: http://www.sciencedirect.com/science/journal/00219991
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution: Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE
French research institutions > Office National d'Etudes et Recherches Aérospatiales - ONERA
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Deposited By:Jeremie Gressier

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