论文信息 - Finite volume transport schemes

Finite volume transport schemes

We analyze arbitrary order linear finite volume transport schemes and show asymptotic stability in L1 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 L1. A scheme of order three is proved to be stable in L1 and L∞.

Bruno Després | B. Després

[1] R. D. Richtmyer,et al. Difference methods for initial-value problems , 1959 .

[2] Michael Dumbser,et al. Fast high order ADER schemes for linear hyperbolic equations , 2004 .

[3] C. Bailly,et al. Numerical Solution of Acoustic Propagation Problems Using linearized Euler's Equations* , 2000 .

[4] Burton Wendroff,et al. On the stability of difference schemes , 1962 .

[5] Robert F. Warming,et al. Recent advances in the development of implicit schemes for the equations of fluid dynamics , 1981 .

[6] Stéphane Del Pino,et al. Arbitrary high-order schemes for the linear advection and wave equations: application to hydrodynamics and aeroacoustics , 2006 .