an:06147565
Zbl 1263.76048
B??rger, Raimund; Karlsen, Kenneth H.; Towers, John D.
On some difference schemes and entropy conditions for a class of multi-species kinematic flow models with discontinuous flux
EN
Netw. Heterog. Media 5, No. 3, 461-485 (2010).
00315971
2010
j
76M25 65M06 76T99 90B20
difference schemes; entropy condition; systems of conservation laws; discontinuous flux; multi-species kinematric flow model
Summary: We study a system of conservation laws that describes multi-species kinematic flows with an emphasis on models of multiclass traffic flow and of the creaming of oil-in-water dispersions. The flux can have a spatial discontinuity which models abrupt changes of road surface conditions or of the cross-sectional area in a settling vessel. For this system, an entropy inequality is proposed that singles out a relevant solution at the interface. It is shown that ``piecewise smooth'' limit solutions generated by the semi-discrete version of a numerical scheme the authors recently proposed [\textit{R. B??rger, A. Garc??a, K. H. Karlsen} and \textit{J. D. Towers}, J. Eng. Math. 60, No. 3--4, 387--425 (2008; Zbl 1200.76126)] satisfy this entropy inequality. We present an improvement to this scheme by means of a special interface flux that is activated only at a few grid points where the discontinuity is located. While an entropy inequality is established for the semi-discrete versions of the scheme only, numerical experiments support that the fully discrete scheme are equally entropy-admissible.
Zbl 1200.76126