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Published October 1, 2011 | public
Journal Article

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

Abstract

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.

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.

Additional details

Created:
August 22, 2023
Modified:
October 24, 2023