Title :

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

Author(s) :

Andreianov, Boris [Auteur]
Laboratoire de Mathématiques de Besançon (UMR 6623) [LMB]
Cancès, Clément [Auteur]
Laboratoire Jacques-Louis Lions [LJLL]
Reliable numerical approximations of dissipative systems [RAPSODI]

Journal title :

Journal of Hyperbolic Differential Equations

Pages :

343-384

Publisher :

World Scientific Publishing

Publication date :

2015-07-15

ISSN :

0219-8916

English keyword(s) :

discontinuous flux
hyperbolic conservation law
monotone finite volume scheme
interface coupling
boundary layer
convergent scheme
well-posedness
entropy solution
interface flux

HAL domain(s) :

Mathématiques [math]/Equations aux dérivées partielles [math.AP]
Mathématiques [math]/Analyse numérique [math.NA]

English abstract : [en]

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 ...
Show more >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.Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

Thématiques actuelles en lois de conservation

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL