The DOI matches its Crossref record; 18 of the 18 references it cites were found in a registry or an index.
High-order Finite Difference and Finite Volume WENO Schemes and Discontinuous Galerkin Methods for CFD
Abstract
In recent years, high order numerical methods have been widely used in computational fluid dynamics (CFD), to effectively resolve complex flow features using meshes which are reasonable for today's computers. In this paper, we review and compare three types of high order methods being used in CFD, namely the weighted essentially non-oscillatory (WENO) finite difference methods, the WENO finite volume methods, and the discontinuous Galerkin (DG) finite element methods. We summarize the main features of these methods, from a practical user's point of view, indicate their applicability and relative strength, and show a few selected numerical examples to demonstrate their performance on illustrative model CFD problems.
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Citations
Cites
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
Self-citationApproximate 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
Self-citationEfficient 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
Self-citationWeighted 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
A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws
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Local adaptive mesh refinement for shock hydrodynamics
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Strong Stability-Preserving High-Order Time Discretization Methods
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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
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
- International Journal of Computational Fluid Dynamics
- Publisher
- Informa UK Limited
- Published
- 2003-03
- Volume
- 17
- Issue
- 2
- Pages
- 107-118
- ISSN
- 1026-7417 (ISSN-L)
- 1061-8562
- 1029-0257
- OpenAlex
- W2049514147
- Cited by
- 469
- References
- 18
- FWCI
- 14.82
- Type
- journal article
- Language
- en
- Open access
- closed
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