21764 articles – 15575 Notices  [english version]
 Fiche détaillée Articles dans des revues avec comité de lecture
 Applied Mathematics Letters 25 (2012) 1844--1848
 Versions disponibles : v1 (12-10-2011) v2 (07-03-2012)
Liste des fichiers attachés à ce document :
 PDF
 Godunov_disc_flux_HAL2.pdf(202.5 KB)
 The Godunov scheme for scalar conservation laws with discontinuous bell-shaped flux functions
 We consider hyperbolic scalar conservation laws with discontinuous flux function of the type $$\partial_t u + \partial_x f(x,u) = 0 \text{\;\;with\;\;} f(x,u) = f_L(u) \Char_{\R^-}(x) + f_R(u) \Char_{\R^+}(x).$$ Here $f_{L,R}$ are compatible bell-shaped flux functions as appear in numerous applications. It was shown by Adimurthi, S. Mishra, G. D. V. Gowda ({\it J. Hyperbolic Differ. Equ. 2 (4) (2005) 783-837)} and R. Bürger, K. H. Karlsen and J. D. Towers ({\it SIAM J. Numer. Anal. 47~(3) (2009) 1684--1712}) that several notions of solution make sense, according to a choice of the so-called $(A,B)$-connection. In this note, we remark that every choice of connection $(A,B)$ corresponds to a limitation of the flux under the form $f(u)|_{x=0}\leq \bar F$, first introduced by R. M. Colombo and P. Goatin ({\it J. Differential Equations 234 (2) (2007) 654-675}). Hence we derive a very simple and cheap to compute explicit formula for the Godunov numerical flux across the interface $\{x=0\}$, for each choice of connection. This gives a simple-to-use numerical scheme governed only by the parameter $\bar F$. A numerical illustration is provided.
 Mots Clés : Scalar conservation laws – discontinuous flux functions – flux limitation – Godunov scheme – $L^1$ dissipative germs
 hal-00631586, version 2 http://hal.archives-ouvertes.fr/hal-00631586 oai:hal.archives-ouvertes.fr:hal-00631586 Contributeur : Clément Cancès <> Soumis le : Mercredi 7 Mars 2012, 11:31:25 Dernière modification le : Mercredi 29 Août 2012, 10:57:57