Journal
JOURNAL OF SCIENTIFIC COMPUTING
Volume 56, Issue 2, Pages 267-290Publisher
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10915-012-9677-5
Keywords
Hyperbolic systems of conservation and balance laws; Saint-Venant system of shallow water equations; Finite volume methods; Well-balanced schemes; Positivity preserving schemes; Wet/dry fronts
Categories
Funding
- NSF [DMS-1115718]
- ONR [N000141210833]
- DFG [NO361/3-1, No361/3-2]
- National Natural Science Foundation of China [11001211, 51178359]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1115718] Funding Source: National Science Foundation
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In this paper, we construct a well-balanced, positivity preserving finite volume scheme for the shallow water equations based on a continuous, piecewise linear discretization of the bottom topography. The main new technique is a special reconstruction of the flow variables in wet-dry cells, which is presented in this paper for the one dimensional case. We realize the new reconstruction in the framework of the second-order semi-discrete central-upwind scheme from (Kurganov and Petrova, Commun. Math. Sci., 5(1):133-160, 2007). The positivity of the computed water height is ensured following (Bollermann et al., Commun. Comput. Phys., 10:371-404, 2011): The outgoing fluxes are limited in case of draining cells.
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