article

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

Authors:

Khosro Shahbazi,

Oscar P. Bruno,

Jan S. HesthavenAuthors Info & Claims

Journal of Computational Physics, Volume 230, Issue 24

Pages 8779 - 8796

https://doi.org/10.1016/j.jcp.2011.08.024

Published: 01 October 2011 Publication History

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.

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Cited By

Shi RJung J(2018)A Domain Decomposition Fourier Continuation Method for Enhanced $$L_1$$L1 Regularization Using Sparsity of Edges in Reconstructing Fourier DataJournal of Scientific Computing10.1007/s10915-017-0467-y74:2(851-871)Online publication date: 1-Feb-2018
https://dl.acm.org/doi/10.1007/s10915-017-0467-y
Shahbazi K(2017)Robust second-order scheme for multi-phase flow computationsJournal of Computational Physics10.1016/j.jcp.2017.03.025339:C(163-178)Online publication date: 15-Jun-2017
https://dl.acm.org/doi/10.1016/j.jcp.2017.03.025
Guo JJung J(2017)A numerical study of the local monotone polynomial edge detection for the hybrid WENO methodJournal of Computational and Applied Mathematics10.1016/j.cam.2017.02.029321:C(232-245)Online publication date: 1-Sep-2017
https://dl.acm.org/doi/10.1016/j.cam.2017.02.029
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Multi-domain Fourier-continuation/WENO hybrid solver for conservation laws
1. Mathematics of computing
  1. Mathematical analysis
    1. Differential equations
2. Theory of computation

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Published In

cover image Journal of Computational Physics

Journal of Computational Physics Volume 230, Issue 24

October, 2011

189 pages

ISSN:0021-9991

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Copyright © Elsevier Inc. © 2011.

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Academic Press Professional, Inc.

United States

Publication History

Published: 01 October 2011

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Cited By

Shi RJung J(2018)A Domain Decomposition Fourier Continuation Method for Enhanced $$L_1$$L1 Regularization Using Sparsity of Edges in Reconstructing Fourier DataJournal of Scientific Computing10.1007/s10915-017-0467-y74:2(851-871)Online publication date: 1-Feb-2018
https://dl.acm.org/doi/10.1007/s10915-017-0467-y
Shahbazi K(2017)Robust second-order scheme for multi-phase flow computationsJournal of Computational Physics10.1016/j.jcp.2017.03.025339:C(163-178)Online publication date: 15-Jun-2017
https://dl.acm.org/doi/10.1016/j.jcp.2017.03.025
Guo JJung J(2017)A numerical study of the local monotone polynomial edge detection for the hybrid WENO methodJournal of Computational and Applied Mathematics10.1016/j.cam.2017.02.029321:C(232-245)Online publication date: 1-Sep-2017
https://dl.acm.org/doi/10.1016/j.cam.2017.02.029
Amlani FBruno O(2016)An FC-based spectral solver for elastodynamic problems in general three-dimensional domainsJournal of Computational Physics10.1016/j.jcp.2015.11.060307:C(333-354)Online publication date: 15-Feb-2016
https://dl.acm.org/doi/10.1016/j.jcp.2015.11.060
Li PGao ZDon WXie S(2015)Hybrid Fourier-Continuation Method and Weighted Essentially Non-oscillatory Finite Difference Scheme for Hyperbolic Conservation Laws in a Single-Domain FrameworkJournal of Scientific Computing10.1007/s10915-014-9913-264:3(670-695)Online publication date: 1-Sep-2015
https://dl.acm.org/doi/10.1007/s10915-014-9913-2
Lyon MPicard J(2014)The Fourier approximation of smooth but non-periodic functions from unevenly spaced dataAdvances in Computational Mathematics10.1007/s10444-014-9342-740:5-6(1073-1092)Online publication date: 1-Dec-2014
https://dl.acm.org/doi/10.1007/s10444-014-9342-7
Shahbazi KHesthaven JZhu X(2013)Multi-dimensional hybrid Fourier continuation-WENO solvers for conservation lawsJournal of Computational Physics10.5555/2743135.2743305253:C(209-225)Online publication date: 15-Nov-2013
https://dl.acm.org/doi/10.5555/2743135.2743305

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