On conservation laws with discontinuous flux. (English) Zbl 1076.76069

Bürger, Raimund; Karlsen, Kenneth H.; Mishra, Siddharta; Towers, John D.

Wang, Yongqi (ed.) et al., Trends in applications of mathematics to mechanics. Proceedings of the international symposium, STAMM, Seeheim, Germany, August 22–28, 2004. Aachen: Shaker (ISBN 3-8322-3600-7/pbk). Berichte aus der Mathematik, 75-84 (2005).

The authors consider two different conservation laws with discontinuous flux defined in two adjacent domains: \(u_t+f(u)_x=0\) for \(x > 0\), and \(u_t+g(u)_x = 0\), for \(x < 0\), \(t > 0\). Their applications include models of two-phase flow in porous media, traffic flows with discontinuous road surface, and clarifier-thickener models of continuous sedimentation. The main difficulty consists in the formulation of a jump criterion for the solution across the flux discontinuity. The authors introduce the entropy solution concept and present numerical schemes to treat the problem.
For the entire collection see [Zbl 1054.74003].

Reviewer: Boris V. Loginov (Ul’yanovsk)

MSC:

76S05	Flows in porous media; filtration; seepage
76T30	Three or more component flows
74S30	Other numerical methods in solid mechanics (MSC2010)
35L65	Hyperbolic conservation laws

Keywords:

entropy solution; two-phase flow; porous media; clarifier-thickener models