Well-balanced positivity preserving central-upwind scheme on triangular grids for the Saint-Venant system

Bryson, Steve; Epshteyn, Yekaterina; Kurganov, Alexander; Petrova, Guergana

Well-balanced positivity preserving central-upwind scheme on triangular grids for the Saint-Venant system

Type

Article

Authors

Bryson, Steve
Epshteyn, Yekaterina
Kurganov, Alexander
Petrova, Guergana

KAUST Grant Number

KUS-C1-016-04

Online Publication Date

2010-10-11

Print Publication Date

2011-05

Date

2010-10-11

Abstract

We introduce a new second-order central-upwind scheme for the Saint-Venant system of shallow water equations on triangular grids. We prove that the scheme both preserves "lake at rest" steady states and guarantees the positivity of the computed fluid depth. Moreover, it can be applied to models with discontinuous bottom topography and irregular channel widths. We demonstrate these features of the new scheme, as well as its high resolution and robustness in a number of numerical examples. © EDP Sciences, SMAI, 2010.

Citation

Bryson S, Epshteyn Y, Kurganov A, Petrova G (2010) Well-balanced positivity preserving central-upwind scheme on triangular grids for the Saint-Venant system. ESAIM: Mathematical Modelling and Numerical Analysis 45: 423–446. Available: http://dx.doi.org/10.1051/m2an/2010060.

Acknowledgements

The research of Y. Epshteyn is based upon work supported by the Center for Nonlinear Analysis (CNA) under the NSF Grant # DMS-0635983. The research of A. Kurganov was supported in part by the NSF Grant # DMS-0610430. The research of G. Petrova was supported in part by the NSF Grant # DMS-0810869 and Award # KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST).