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Multi-domain Fourier-continuation/WENO hybrid solver for conservation laws

Shahbazi, Khosro and Albin, Nathan and Bruno, Oscar P. and Hesthaven, Jan S. (2011) Multi-domain Fourier-continuation/WENO hybrid solver for conservation laws. Journal of Computational Physics, 230 (24). pp. 8779-8796. ISSN 0021-9991.

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We introduce a multi-domain Fourier-continuation/WENO hybrid method (FC–WENO) that enables high-order and non-oscillatory solution of systems of nonlinear conservation laws, and which enjoys essentially dispersionless, spectral character away from discontinuities, as well as mild CFL constraints (comparable to those of finite difference methods). The hybrid scheme employs the expensive, shock-capturing WENO method in small regions containing discontinuities and the efficient FC method in the rest of the computational domain, yielding a highly effective overall scheme for applications with a mix of discontinuities and complex smooth structures. The smooth and discontinuous solution regions are distinguished using the multi-resolution procedure of Harten [J. Comput. Phys. 115 (1994) 319–338]. We consider WENO schemes of formal orders five and nine and a FC method of order five. The accuracy, stability and efficiency of the new hybrid method for conservation laws is investigated for problems with both smooth and non-smooth solutions. In the latter case, we solve the Euler equations for gas dynamics for the standard test case of a Mach three shock wave interacting with an entropy wave, as well as a shock wave (with Mach 1.25, three or six) interacting with a very small entropy wave and evaluate the efficiency of the hybrid FC–WENO method as compared to a purely WENO-based approach as well as alternative hybrid based techniques. We demonstrate considerable computational advantages of the new FC-based method, suggesting a potential of an order of magnitude acceleration over alternatives when extended to fully three-dimensional problems.

Item Type:Article
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Bruno, Oscar P.0000-0001-8369-3014
Additional Information:© 2011 Elsevier Inc. Received 18 October 2010; revised 26 August 2011; Accepted 28 August 2011. Available online 7 September 2011. This work was financially supported by US Department of Energy, under Contract DE-FG02-98ER25346. N.A. and O.B. gratefully acknowledge support from AFOSR and NSF. The careful reading and excellent comments by reviewers are highly appreciated.
Funding AgencyGrant Number
Department of Energy (DOE)DE-FG02-98ER25346
Air Force Office of Scientific Research (AFOSR)UNSPECIFIED
Subject Keywords:Fourier continuation methods; High-order WENO methods; Multi-resolution methods; Conservation laws; Shock waves
Issue or Number:24
Record Number:CaltechAUTHORS:20111212-085019337
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Official Citation:Khosro Shahbazi, Nathan Albin, Oscar P. Bruno, Jan S. Hesthaven, Multi-domain Fourier-continuation/WENO hybrid solver for conservation laws, Journal of Computational Physics, Volume 230, Issue 24, 1 October 2011, Pages 8779-8796, ISSN 0021-9991, 10.1016/
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:28413
Deposited By: Tony Diaz
Deposited On:14 Dec 2011 16:30
Last Modified:09 Mar 2020 13:18

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