Naslov
On different flux splittings and flux functions in WENO schemes for balance laws

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

Izvornik
Computers & Fluids (0045-7930) 35 (2006), 10; 1074-1092

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

Ključne riječi
finite difference WENO schemes; finite volume WENO schemes; hyperbolic balance law; shallow water equations; open--channel flow equations; balanced numerical schemes

Sažetak
In this paper we focus our attention on obtaining well balanced schemes for balance laws by using Marquina's flux in combination with the finite difference and finite volume WENO schemes. We consider also the Rusanov flux splitting and the HLL approximate Riemann solver. In particular, for the presented numerical schemes we develop corresponding discretizations of the source term, based on the idea of balancing with the flux gradient. When applied to the open--channel flow and to the shallow water equations, we obtain the finite difference WENO scheme with Marquina's flux splitting, which satisfies the approximate conservation property, and also the balanced finite volume WENO scheme with Marquina's solver satisfying the exact conservation property. Finally, we also present an improvement of the balanced finite difference WENO scheme with the Rusanov (locally Lax--Friedrichs) flux splitting, we previously developed.

Izvorni jezik
Engleski

Znanstvena područja
Matematika, Temeljne tehničke znanosti

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