Abstract
We develop well-balanced finite-volume central schemes on overlapping cells for the Saint-Venant shallow water system and its variants. The main challenge in deriving the schemes is related to the fact that the Saint-Venant system contains a geometric source term due to nonflat bottom topography and therefore a delicate balance between the flux gradients and source terms has to be preserved. We propose a constant subtraction technique, which helps one to ensure a well-balanced property of the schemes, while maintaining arbitrary high-order of accuracy. Hierarchical reconstruction limiting procedure is applied to eliminate spurious oscillations without using characteristic decomposition. Extensive one- and two-dimensional numerical simulations are conducted to verify the well-balanced property, high-order of accuracy, and non-oscillatory high-resolution for both smooth and nonsmooth solutions.
Original language | English (US) |
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Pages (from-to) | 678-698 |
Number of pages | 21 |
Journal | Journal of Scientific Computing |
Volume | 63 |
Issue number | 3 |
DOIs | |
State | Published - Jun 1 2015 |
Externally published | Yes |
Bibliographical note
Funding Information:Suo Yang and Yingjie Liu: Research supported in part by NSF Grant DMS-1115671.
Funding Information:
Alexander Kurganov: Research supported in part by NSF Grant DMS-1216957 and ONR Grant N00014-12-1-0833.
Publisher Copyright:
© 2014, Springer Science+Business Media New York.
Keywords
- Balance laws
- Central scheme
- Central schemes on overlapping cells
- Saint-Venant system
- Shallow water
- Well-balanced scheme