The DOI matches its Crossref record; 26 of the 26 references it cites were found in a registry or an index.
Central-Upwind Schemes for the Saint-Venant System
Open accessAbstract
We present one- and two-dimensional central-upwind schemes for approximating solutions of the Saint-Venant system with source terms due to bottom topography. The Saint-Venant system has steady-state solutions in which nonzero flux gradients are exactly balanced by the source terms. It is a challenging problem to preserve this delicate balance with numerical schemes. Small perturbations of these states are also very difficult to compute. Our approach is based on extending semi-discrete central schemes for systems of hyperbolic conservation laws to balance laws. Special attention is paid to the discretization of the source term such as to preserve stationary steady-state solutions. We also prove that the second-order version of our schemes preserves the nonnegativity of the height of the water. This important feature allows one to compute solutions for problems that include dry areas.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method
van Leer, B. (1979) · Journal of Computational Physics · doi:10.1016/0021-9991(79)90145-1 · Cited by 7,142
Efficient implementation of essentially non-oscillatory shock-capturing schemes
Shu, C.-W., & Osher, S. (1988) · Journal of Computational Physics · doi:10.1016/0021-9991(88)90177-5 · Cited by 4,886
Efficient implementation of essentially non-oscillatory shock-capturing schemes, II
Shu, C.-W., & Osher, S. (1989) · Journal of Computational Physics · doi:10.1016/0021-9991(89)90222-2 · Cited by 4,851
Weighted Essentially Non-oscillatory Schemes
Liu, X.-D., Osher, S., & Chan, T. (1994) · Journal of Computational Physics · doi:10.1006/jcph.1994.1187 · Cited by 3,437
Uniformly high order accurate essentially non-oscillatory schemes, III
Harten, A., Engquist, B., Osher, S., & Chakravarthy, S. R. (1987) · Journal of Computational Physics · doi:10.1016/0021-9991(87)90031-3 · Cited by 3,002
High Resolution Schemes Using Flux Limiters for Hyperbolic Conservation Laws
Sweby, P. K. (1984) · SIAM Journal on Numerical Analysis · doi:10.1137/0721062 · Cited by 2,699
Strong Stability-Preserving High-Order Time Discretization Methods
Gottlieb, S., Shu, C.-W., & Tadmor, E. (2001) · SIAM Review · doi:10.1137/s003614450036757x · Cited by 2,565
Kurganov, A., & Tadmor, E. (2000) · Journal of Computational Physics · doi:10.1006/jcph.2000.6459 · Cited by 1,938
Self-citationNon-oscillatory central differencing for hyperbolic conservation laws
Nessyahu, H., & Tadmor, E. (1990) · Journal of Computational Physics · doi:10.1016/0021-9991(90)90260-8 · Cited by 1,246
Total-Variation-Diminishing Time Discretizations
Shu, C.-W. (1988) · SIAM Journal on Scientific and Statistical Computing · doi:10.1137/0909073 · Cited by 1,085
Cited by
Finite-volume schemes for shallow-water equations
Kurganov, A. (2018) · Acta Numerica · doi:10.1017/s0962492918000028 · Cited by 108
Self-citationQi, X., de Almeida, G. A. M., & Maldonado, S. (2024) · Journal of Hydrology · doi:10.1016/j.jhydrol.2024.131263 · Cited by 78
Metadata
- Authors
- Kurganov, A., & Levy, D.
- Venue
- ESAIM: Mathematical Modelling and Numerical Analysis
- Publisher
- EDP Sciences
- Published
- 2002-05
- Volume
- 36
- Issue
- 3
- Pages
- 397-425
- ISSN
- 0764-583X (ISSN-L)
- 1290-3841
- OpenAlex
- W2133429431
- Cited by
- 323
- References
- 26
- FWCI
- 14.90
- Type
- journal article
- Language
- en
- Open access
- bronze
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Central-Upwind Schemes for the Saint-Venant System. https://app.cochat.ai/papers/10.1051/m2an:2002019
- The paper
- Kurganov, A., & Levy, D. (2002). Central-Upwind Schemes for the Saint-Venant System. ESAIM: Mathematical Modelling and Numerical Analysis. https://doi.org/10.1051/m2an%3A2002019
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
