A WELL-BALANCED SCHEME FOR THE NUMERICAL PROCESSING OF SOURCE TERMS IN HYPERBOLIC-EQUATIONS

Citation
Jm. Greenberg et Ay. Leroux, A WELL-BALANCED SCHEME FOR THE NUMERICAL PROCESSING OF SOURCE TERMS IN HYPERBOLIC-EQUATIONS, SIAM journal on numerical analysis, 33(1), 1996, pp. 1-16
Citations number
4
Categorie Soggetti
Mathematics,Mathematics
ISSN journal
00361429
Volume
33
Issue
1
Year of publication
1996
Pages
1 - 16
Database
ISI
SICI code
0036-1429(1996)33:1<1:AWSFTN>2.0.ZU;2-9
Abstract
In a variety of physical problems one encounters source terms that are balanced by internal forces and this balance supports multiple steady state solutions that are stable. Typical of these are gravity-driven flows such as those described by the shallow water equations over a no nuniform ocean bottom. (1.10) h(t)+(hu)(x) = 0 and (hu)(t)+(hu(2)+gh(2 )/2)(x)+ga(x)(x)h = 0; Many classic numerical schemes cannot maintain these steady solutions or achieve them in the long time limit with an acceptable level of accuracy because they do not preserve the proper b alance between the source terms and internal forces. We propose here a numerical scheme, adapted to a scalar conservation law, that preserve s this balance and that can, it is hoped, be extended to more general hyperbolic systems. The proof of convergence of this scheme toward the entropy solution is given and some numerical tests are reported.