The DOI matches its Crossref record; 22 of the 22 references it cites were found in a registry or an index.
Central WENO schemes for hyperbolic systems of conservation laws
Open accessAbstract
We present a family of high-order, essentially non-oscillatory, central schemes for approximating solutions of hyperbolic systems of conservation laws. These schemes are based on a new centered version of the Weighed Essentially Non-Oscillatory (WENO) reconstruction of point-values from cell-averages, which is then followed by an accurate approximation of the fluxes via a natural continuous extension of Runge-Kutta solvers. We explicitly construct the third and fourth-order scheme and demonstrate their high-resolution properties in several numerical tests.
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
Approximate Riemann solvers, parameter vectors, and difference schemes
Roe, P. L. (1981) · Journal of Computational Physics · doi:10.1016/0021-9991(81)90128-5 · Cited by 9,232
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 Weighted ENO Schemes
Jiang, G.-S., & Shu, C.-W. (1996) · Journal of Computational Physics · doi:10.1006/jcph.1996.0130 · Cited by 6,571
Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes
Roe, P. L. (1997) · Journal of Computational Physics · doi:10.1006/jcph.1997.5705 · Cited by 6,277
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
Numerical Methods for Conservation Laws
LeVeque, R. J. (1992) · Birkhäuser Basel eBooks · doi:10.1007/978-3-0348-8629-1 · Cited by 3,632
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
The numerical simulation of two-dimensional fluid flow with strong shocks
Woodward, P., & Colella, P. (1984) · Journal of Computational Physics · doi:10.1016/0021-9991(84)90142-6 · Cited by 2,928
Cited by
High Order Weighted Essentially Nonoscillatory Schemes for Convection Dominated Problems
Shu, C.-W. (2009) · SIAM Review · doi:10.1137/070679065 · Cited by 964
Finite-volume schemes for shallow-water equations
Kurganov, A. (2018) · Acta Numerica · doi:10.1017/s0962492918000028 · Cited by 108
Metadata
- Authors
- Levy, D., Puppo, G., & Russo, G.
- Venue
- ESAIM: Mathematical Modelling and Numerical Analysis
- Publisher
- EDP Sciences
- Published
- 1999-05
- Volume
- 33
- Issue
- 3
- Pages
- 547-571
- ISSN
- 0764-583X (ISSN-L)
- 1290-3841
- OpenAlex
- W2158522603
- Cited by
- 445
- References
- 22
- FWCI
- 9.96
- 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 WENO schemes for hyperbolic systems of conservation laws. https://app.cochat.ai/papers/10.1051/m2an:1999152
- The paper
- Levy, D., Puppo, G., & Russo, G. (1999). Central WENO schemes for hyperbolic systems of conservation laws. ESAIM: Mathematical Modelling and Numerical Analysis. https://doi.org/10.1051/m2an%3A1999152
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.
