Balanced Central NT Schemes for the Shallow Water Equations [chapter]

Nelida Črnjarić-Žic, Senka Vuković, Luka Sopta
Proceedings of the Conference on Applied Mathematics and Scientific Computing  
The numerical method we consider is based on the nonstaggered central scheme proposed by Jiang, Levy, Lin, Osher, and Tadmor (SIAM J. Numer. Anal. 35, 2147 (1998 ) that was obtained by conversion of the standard central NT scheme to the nonstaggered mesh. The generalization we propose is connected with the numerical evaluation of the geometrical source term. The presented scheme is applied to the nonhomogeneous shallow water system. Including an appropriate numerical treatment for the source
more » ... t for the source term evaluation we obtain the scheme that preserves quiescent steady-state for the shallow water equations exactly. We consider two different approaches that depend on the discretization of the riverbed bottom. The obtained schemes are well balanced and present accurate and robust results in both steady and unsteady flow simulations.
doi:10.1007/1-4020-3197-1_11 fatcat:ac4d3nbsezekbiblmuyeyuh2vq