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Discontinuity Diagnosis Essentially Non-Oscillatory Schemes

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Computational Fluid Dynamics 2006
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Abstract

Essentially non-oscillatory (ENO) schemes were first introduced by Harten, Engquist, Osher, and Chakravarthy [1] in the form of cell averages. Later, Shu and Osher [2] [3] developed ENO schemes applying the adaptive stencil idea to the numerical fluxes and using TVD Runge-Kutta type time discretizations.

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References

  1. Harten, A., Engquist, B., Osher, S., Chakravarthy, S.J.: Uniformly high order essentially non-oscillatory schemes, III, J.Comput. Phys. 71, 231, (1987)

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  2. Shu, C.W., Osher, S.: Efficient implementation of essentially non-oscillatory shock capturing schemes, J.Comput. Phys. 77, 439, (1988)

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  3. Shu, C.W., Osher, S.: Efficient implementation of essentially non-oscillatory shock capturing schemes II, J.Comput. Phys. 83, 32, (1989)

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  4. Jiang, G.S., Shu, C.W.: Efficient implementation of weighted ENO schemes, J.Comput. Phys. 126, 202, (1996)

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  5. Steger, J.L., Warming, R.F: Flux vector splitting of the inviscid gasdynamic equations with application to finite-difference methods, J.Comput. Phys. 40, 263, (1981)

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  6. Sod, G.A.: A survey of finite difference methods for systems of nonlinear hyperbolic conservation laws, J.Comput. Phys. 27, 1, (1978)

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Acknowledgements

The authors gratefully acknowledge Professor Chi-Wang Shu for helpful discussions and suggestions about flux-version ENO schemes. We also thank Dr. Hong-Wei Liu at The Hong Kong University of Science and Technology for helpful discussions.

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Correspondence to Yun-Feng Liu .

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Liu, YF., Wang, JP. (2009). Discontinuity Diagnosis Essentially Non-Oscillatory Schemes. In: Deconinck, H., Dick, E. (eds) Computational Fluid Dynamics 2006. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-92779-2_24

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  • DOI: https://doi.org/10.1007/978-3-540-92779-2_24

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