The DOI matches its Crossref record; 8 of the 8 references it cites were found in a registry or an index.
Total-Variation-Diminishing Time Discretizations
Abstract
In the computation of conservation laws $u_t + f(u)_x = 0$, total-variation-diminishing (TVD) schemes have been very successful. Many TVD schemes are of method-of-lines form (i.e., discretized in spatial variables only); hence time discretizations that keep TVD and have other properties (e.g., large CFL numbers for steady state calculations, or high-order accuracy for time-dependent problems) are desirable. In this paper we present a class of m-step Runge–Kutta-type TVD time discretizations with large CFL number m, suitable for steady state calculations, and a class of multilevel type TVD high-order time discretizations suitable for time-dependent problems. Some preliminary numerical results are also given.
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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
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, II
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Self-citationHigh resolution schemes for hyperbolic conservation laws
Harten, A. (1983) · Journal of Computational Physics · doi:10.1016/0021-9991(83)90136-5 · Cited by 4,228
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
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Uniformly High-Order Accurate Nonoscillatory Schemes. I
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Cited by
Shu, C.-W. (1998) · Lecture Notes in Mathematics · doi:10.1007/bfb0096355 · Cited by 1,919
Self-citationA PDE-Based Fast Local Level Set Method
Peng, D., Merriman, B., Osher, S., Zhao, H., & Kang, M. (1999) · Journal of Computational Physics · doi:10.1006/jcph.1999.6345 · Cited by 1,255
High Order Weighted Essentially Nonoscillatory Schemes for Convection Dominated Problems
Shu, C.-W. (2009) · SIAM Review · doi:10.1137/070679065 · Cited by 964
Self-citationFinite-volume schemes for shallow-water equations
Kurganov, A. (2018) · Acta Numerica · doi:10.1017/s0962492918000028 · Cited by 108
Metadata
- Authors
- Shu, C.-W.
- Venue
- SIAM Journal on Scientific and Statistical Computing
- Published
- 1988-11
- Volume
- 9
- Issue
- 6
- Pages
- 1073-1084
- ISSN
- 0196-5204 (ISSN-L)
- 2168-3417
- OpenAlex
- W2093711514
- Cited by
- 1,085
- References
- 8
- FWCI
- 3.05
- Type
- journal article
- Language
- en
- Open access
- closed
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