# On interface transmission conditions for conservation laws with discontinuous flux of general shape

3 RAPSODI - Reliable numerical approximations of dissipative systems
LPP - Laboratoire Paul Painlevé - UMR 8524, Inria Lille - Nord Europe
Abstract : Conservation laws of the form $\partial_t u+ \partial_x f(x;u)=0$ with space-discontinuous flux $f(x;\cdot)=f_l(\cdot)\mathbf{1}_{x<0}+f_r(\cdot)\mathbf{1}_{x>0}$ were deeply investigated in the last ten years, with a particular emphasis in the case where the fluxes are ''bell-shaped". In this paper, we introduce and exploit the idea of transmission maps for the interface condition at the discontinuity, leading to the well-posedness for the Cauchy problem with general shape of $f_{l,r}$. The design and the convergence of monotone Finite Volume schemes based on one-sided approximate Riemann solvers is then assessed. We conclude the paper by illustrating our approach by several examples coming from real-life applications.
Keywords :
Domain :

Cited literature [67 references]

https://hal.archives-ouvertes.fr/hal-00940756
Contributor : Boris Andreianov <>
Submitted on : Friday, July 4, 2014 - 3:19:50 PM
Last modification on : Saturday, March 28, 2020 - 2:19:15 AM
Document(s) archivé(s) le : Saturday, October 4, 2014 - 12:41:10 PM

### File

AC-NBS-PreprintVers2.pdf
Files produced by the author(s)

### Citation

Boris Andreianov, Clément Cancès. On interface transmission conditions for conservation laws with discontinuous flux of general shape. Journal of Hyperbolic Differential Equations, World Scientific Publishing, 2015, 12 (2), pp.343-384. ⟨10.1142/S0219891615500101⟩. ⟨hal-00940756v2⟩

Record views