Abstract
A systematic approach for constructing Energy Stable Weighted Essentially Non-Oscillatory (ESWENO) finite difference schemes of arbitrary order is presented. The new class of schemes is proven to be stable in the energy norm for both continuous and discontinuous solutions of systems of linear hyperbolic equations. We also present new weight functions and constraints on their parameters, which provide consistency and much faster convergence of the high-order ESWENO schemes to their underlying linear schemes. Furthermore, the improved weight functions guarantee that the ESWENO schemes are design-order accurate for smooth solutions with arbitrary number of vanishing derivatives and provide much better resolution near strong discontinuities than the conventional counterparts. Numerical results show that the new ESWENO schemes are stable and significantly outperform the corresponding WENO schemes of Jiang and Shu in terms of accuracy, while providing essentially non-oscillatory solutions near strong discontinuities.
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References
Jiang, G., Shu, C.-W.: Efficient implementation of weighted ENO schemes. J. Comput. Phys. 126 202–228 (1996)
Yamaleev, N.K., and Carpenter, M.H.: Third-order energy stable WENO scheme. J. Comput. Phys. 228(8), 3025–3047 (2009)
Yamaleev, N.K., Carpenter, M.H.: A systematic methodology for constructing high-order Energy Stable WENO Schemes. J. Comput. Phys. 228(11), 4248–4272 (2009)
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© 2011 Springer-Verlag Berlin Heidelberg
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Yamaleev, N.K., Carpenter, M. (2011). Energy Stable WENO Schemes of Arbitrary Order. In: Kuzmin, A. (eds) Computational Fluid Dynamics 2010. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17884-9_8
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DOI: https://doi.org/10.1007/978-3-642-17884-9_8
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Online ISBN: 978-3-642-17884-9
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