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 non-oscillatory 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.
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Acknowledgements
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.
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Niu, Y., Gao, Z., Don, W.S., Xie, S., Li, P. (2015). Hybrid Compact-WENO Finite Difference Scheme For Detonation Waves Simulations. In: Kirby, R., Berzins, M., Hesthaven, J. (eds) Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014. Lecture Notes in Computational Science and Engineering, vol 106. Springer, Cham. https://doi.org/10.1007/978-3-319-19800-2_14
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DOI: https://doi.org/10.1007/978-3-319-19800-2_14
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