Naslov
WENO Schemes for Balance Laws with Spatially Varying Flux

Autori
Vuković, Senka ; Črnjarić-Žic, Nelida ; Sopta, Luka

Izvornik
Journal of Computational Physics (0021-9991) 199 (2004); 87-109

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
hyperbolic balance laws; spatially varying flux; flux gradient and source term balancing; open channel flow equations; elastic wave equations

Sažetak
In this paper we are concerned with the construction of numerical schemes of high order of accuracy for hyperbolic balance law systems with spatially variable flux function, as well as with a source term of geometrical type. We start with the original finite difference componentwise weighted essentially nonoscillatory (WENO) schemes and then we create new schemes by modifying the flux formulations (locally Lax-Friedrichs and Roe with entropy fix) since flux is spatially variable, and by decomposing the source term in order to obtain balance between numerical approximations of the flux gradient and of the source term. We apply so extended WENO schemes to one-dimensional open channel flow equations and one-dimensional elastic wave equations. In particular, we prove that in these applications the new schemes are exactly consistent with appropriately chosen subset of steady state solutions. Experimentally obtained orders of accuracy of the extended and original WENO schemes result to be almost identical. Test problem results illustrate the improvement of the proposed schemes relative to original WENO schemes combined with pointwise source term evaluation. As expected, the increase in the formal order of accuracy of applied WENO reconstructions in all the test problems causes visible increase in the high resolution properties of the schemes.

Izvorni jezik
Engleski

Znanstvena područja
Matematika, Temeljne tehničke znanosti

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