Hybrid Compact-WENO Finite Difference Scheme For Detonation Waves Simulations

Yanpo Niu; Zhen Gao; Wai Sun Don; Shusen Xie; Peng Li

doi:10.1007/978-3-319-19800-2_14

Hybrid Compact-WENO Finite Difference Scheme For Detonation Waves Simulations

Yanpo Niu, Zhen Gao, Wai Sun Don^*, Shusen Xie, Peng Li

^*Corresponding author for this work

Research output: Chapter in book/report/conference proceeding › Conference proceeding › peer-review

4 Citations (Scopus)

Abstract

The performance of a hybrid compact (Compact) finite difference scheme and characteristic-wise weighted essentially non-oscillatory (WENO) finite difference scheme (Hybrid) for the detonation waves simulations is investigated. The Hybrid scheme employs the nonlinear 5th-order WENO-Z scheme to capture high gradients and discontinuities in an essentially nonoscillatory manner and the linear 6th-order Compact scheme to resolve the fine scale structures in the smooth regions of the solution in an efficient and accurate manner. Numerical oscillations generated by the Compact scheme is mitigated by the high order filtering. The high order multi-resolution algorithm is employed to detect the smoothness of the solution. The Hybrid scheme allows a potential speedup up to a factor of three or more for certain classes of shocked problems. The simulations of one-dimensional shock-entropy wave interaction and classical stable detonation waves, and the two-dimensional detonation diffraction problem around a 90° corner show that the Hybrid scheme is more efficient, less dispersive and less dissipative than the WENO-Z scheme.

Original language	English
Title of host publication	Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014
Subtitle of host publication	Selected papers from the ICOSAHOM conference, June 23-27, 2014, Salt Lake City, Utah, USA
Editors	Robert M. Kirby, Martin Berzins, Jan S. Hesthaven
Publisher	Springer Cham
Pages	179-187
Number of pages	9
Edition	1st
ISBN (Electronic)	9783319198002
ISBN (Print)	9783319197999
DOIs	https://doi.org/10.1007/978-3-319-19800-2_14
Publication status	Published - 26 Nov 2015
Externally published	Yes
Event	10th International Conference on Spectral and High-Order Methods, ICOSAHOM 2014 - Salt Lake City, United States Duration: 23 Jun 2014 → 27 Jun 2014 https://link.springer.com/book/10.1007/978-3-319-19800-2 (Conference proceedings)

Publication series

Name	Lecture Notes in Computational Science and Engineering
Volume	106
ISSN (Print)	1439-7358
ISSN (Electronic)	2197-7100

Conference

Conference	10th International Conference on Spectral and High-Order Methods, ICOSAHOM 2014
Country/Territory	United States
City	Salt Lake City
Period	23/06/14 → 27/06/14
Internet address	https://link.springer.com/book/10.1007/978-3-319-19800-2 (Conference proceedings)

User-Defined Keywords

Detonation Wave
Finite Difference Scheme
Hybrid Scheme
Detonation Front
WENO Scheme

Access to Document

10.1007/978-3-319-19800-2_14

Cite this

Niu, Y., Gao, Z., Don, W. S., Xie, S., & Li, P. (2015). Hybrid Compact-WENO Finite Difference Scheme For Detonation Waves Simulations. In R. M. Kirby, M. Berzins, & J. S. Hesthaven (Eds.), Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014: Selected papers from the ICOSAHOM conference, June 23-27, 2014, Salt Lake City, Utah, USA (1st ed., pp. 179-187). (Lecture Notes in Computational Science and Engineering; Vol. 106). Springer Cham. https://doi.org/10.1007/978-3-319-19800-2_14

Niu, Yanpo ; Gao, Zhen ; Don, Wai Sun et al. / Hybrid Compact-WENO Finite Difference Scheme For Detonation Waves Simulations. Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014: Selected papers from the ICOSAHOM conference, June 23-27, 2014, Salt Lake City, Utah, USA. editor / Robert M. Kirby ; Martin Berzins ; Jan S. Hesthaven. 1st. ed. Springer Cham, 2015. pp. 179-187 (Lecture Notes in Computational Science and Engineering).

@inproceedings{74f6754afaef4467903b3fde522c67da,

title = "Hybrid Compact-WENO Finite Difference Scheme For Detonation Waves Simulations",

abstract = "The performance of a hybrid compact (Compact) finite difference scheme and characteristic-wise weighted essentially non-oscillatory (WENO) finite difference scheme (Hybrid) for the detonation waves simulations is investigated. The Hybrid scheme employs the nonlinear 5th-order WENO-Z scheme to capture high gradients and discontinuities in an essentially nonoscillatory manner and the linear 6th-order Compact scheme to resolve the fine scale structures in the smooth regions of the solution in an efficient and accurate manner. Numerical oscillations generated by the Compact scheme is mitigated by the high order filtering. The high order multi-resolution algorithm is employed to detect the smoothness of the solution. The Hybrid scheme allows a potential speedup up to a factor of three or more for certain classes of shocked problems. The simulations of one-dimensional shock-entropy wave interaction and classical stable detonation waves, and the two-dimensional detonation diffraction problem around a 90° corner show that the Hybrid scheme is more efficient, less dispersive and less dissipative than the WENO-Z scheme.",

keywords = "Detonation Wave, Finite Difference Scheme, Hybrid Scheme, Detonation Front, WENO Scheme",

author = "Yanpo Niu and Zhen Gao and Don, {Wai Sun} and Shusen Xie and Peng Li",

note = "The authors would like to acknowledge the funding support of this research by National Natural Science Foundation of China (11201441), China Postdoctoral Science Foundation (2012M521374, 2013T60684) and Fundamental Research Funds for the Central Universities (201362033). The author (Don) also likes to thank the Ocean University of China for providing the startup fund (201412003) that is used to support this work. Part of the work was performed during the Second Summer Workshop of Advanced Research in Applied Mathematics and Scientific Computing 2014 and the authors are grateful for the support provided by the School of Mathematical Sciences at Ocean University of China. Publisher Copyright: {\textcopyright} Springer International Publishing Switzerland 2015.; 10th International Conference on Spectral and High-Order Methods, ICOSAHOM 2014 ; Conference date: 23-06-2014 Through 27-06-2014",

year = "2015",

month = nov,

day = "26",

doi = "10.1007/978-3-319-19800-2_14",

language = "English",

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publisher = "Springer Cham",

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Niu, Y, Gao, Z, Don, WS, Xie, S & Li, P 2015, Hybrid Compact-WENO Finite Difference Scheme For Detonation Waves Simulations. in RM Kirby, M Berzins & JS Hesthaven (eds), Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014: Selected papers from the ICOSAHOM conference, June 23-27, 2014, Salt Lake City, Utah, USA. 1st edn, Lecture Notes in Computational Science and Engineering, vol. 106, Springer Cham, pp. 179-187, 10th International Conference on Spectral and High-Order Methods, ICOSAHOM 2014, Salt Lake City, Utah, United States, 23/06/14. https://doi.org/10.1007/978-3-319-19800-2_14

Hybrid Compact-WENO Finite Difference Scheme For Detonation Waves Simulations. / Niu, Yanpo; Gao, Zhen; Don, Wai Sun et al.
Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014: Selected papers from the ICOSAHOM conference, June 23-27, 2014, Salt Lake City, Utah, USA. ed. / Robert M. Kirby; Martin Berzins; Jan S. Hesthaven. 1st. ed. Springer Cham, 2015. p. 179-187 (Lecture Notes in Computational Science and Engineering; Vol. 106).

Research output: Chapter in book/report/conference proceeding › Conference proceeding › peer-review

TY - GEN

T1 - Hybrid Compact-WENO Finite Difference Scheme For Detonation Waves Simulations

AU - Niu, Yanpo

AU - Gao, Zhen

AU - Don, Wai Sun

AU - Xie, Shusen

AU - Li, Peng

N1 - The authors would like to acknowledge the funding support of this research by National Natural Science Foundation of China (11201441), China Postdoctoral Science Foundation (2012M521374, 2013T60684) and Fundamental Research Funds for the Central Universities (201362033). The author (Don) also likes to thank the Ocean University of China for providing the startup fund (201412003) that is used to support this work. Part of the work was performed during the Second Summer Workshop of Advanced Research in Applied Mathematics and Scientific Computing 2014 and the authors are grateful for the support provided by the School of Mathematical Sciences at Ocean University of China. Publisher Copyright: © Springer International Publishing Switzerland 2015.

PY - 2015/11/26

Y1 - 2015/11/26

N2 - The performance of a hybrid compact (Compact) finite difference scheme and characteristic-wise weighted essentially non-oscillatory (WENO) finite difference scheme (Hybrid) for the detonation waves simulations is investigated. The Hybrid scheme employs the nonlinear 5th-order WENO-Z scheme to capture high gradients and discontinuities in an essentially nonoscillatory manner and the linear 6th-order Compact scheme to resolve the fine scale structures in the smooth regions of the solution in an efficient and accurate manner. Numerical oscillations generated by the Compact scheme is mitigated by the high order filtering. The high order multi-resolution algorithm is employed to detect the smoothness of the solution. The Hybrid scheme allows a potential speedup up to a factor of three or more for certain classes of shocked problems. The simulations of one-dimensional shock-entropy wave interaction and classical stable detonation waves, and the two-dimensional detonation diffraction problem around a 90° corner show that the Hybrid scheme is more efficient, less dispersive and less dissipative than the WENO-Z scheme.

AB - The performance of a hybrid compact (Compact) finite difference scheme and characteristic-wise weighted essentially non-oscillatory (WENO) finite difference scheme (Hybrid) for the detonation waves simulations is investigated. The Hybrid scheme employs the nonlinear 5th-order WENO-Z scheme to capture high gradients and discontinuities in an essentially nonoscillatory manner and the linear 6th-order Compact scheme to resolve the fine scale structures in the smooth regions of the solution in an efficient and accurate manner. Numerical oscillations generated by the Compact scheme is mitigated by the high order filtering. The high order multi-resolution algorithm is employed to detect the smoothness of the solution. The Hybrid scheme allows a potential speedup up to a factor of three or more for certain classes of shocked problems. The simulations of one-dimensional shock-entropy wave interaction and classical stable detonation waves, and the two-dimensional detonation diffraction problem around a 90° corner show that the Hybrid scheme is more efficient, less dispersive and less dissipative than the WENO-Z scheme.

KW - Detonation Wave

KW - Finite Difference Scheme

KW - Hybrid Scheme

KW - Detonation Front

KW - WENO Scheme

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SN - 9783319197999

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BT - Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014

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Niu Y, Gao Z, Don WS, Xie S, Li P. Hybrid Compact-WENO Finite Difference Scheme For Detonation Waves Simulations. In Kirby RM, Berzins M, Hesthaven JS, editors, Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014: Selected papers from the ICOSAHOM conference, June 23-27, 2014, Salt Lake City, Utah, USA. 1st ed. Springer Cham. 2015. p. 179-187. (Lecture Notes in Computational Science and Engineering). doi: 10.1007/978-3-319-19800-2_14

Hybrid Compact-WENO Finite Difference Scheme For Detonation Waves Simulations

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