Finite volume transport schemes

Authors:
Bruno Després_aff1n2
Affiliations:
af1 CEA/DIF, Bruyères le Chatel, 91297, Arpajon Cedex, France
Venue:
Numerische Mathematik
Year:
2008

Citing 0
Cited 2

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Abstract

We analyze arbitrary order linear finite volume transport schemes and show asymptotic stability in L 1 and L ∞ for odd order schemes in dimension one. It gives sharp fractional order estimates of convergence for BV solutions. It shows odd order finite volume advection schemes are better than even order finite volume schemes. Therefore the Gibbs phenomena is controlled for odd order finite volume schemes. Numerical experiments sustain the theoretical analysis. In particular the oscillations of the Lax–Wendroff scheme for small Courant numbers are correlated with its non stability in L 1. A scheme of order three is proved to be stable in L 1 and L ∞.