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FC-based shock-dynamics solver with neural-network localized artificial-viscosity assignment

Bruno, Oscar P. and Hesthaven, Jan S. and Leibovici, Daniel V. (2022) FC-based shock-dynamics solver with neural-network localized artificial-viscosity assignment. Journal of Computational Physics: X, 15 . Art. No. 100110. ISSN 2590-0552. doi:10.1016/j.jcpx.2022.100110.

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This paper presents a spectral scheme for the numerical solution of nonlinear conservation laws in non-periodic domains under arbitrary boundary conditions. The approach relies on the use of the Fourier Continuation (FC) method for spectral representation of non-periodic functions in conjunction with smooth localized artificial viscosity assignments produced by means of a Shock-Detecting Neural Network (SDNN). Like previous shock capturing schemes and artificial viscosity techniques, the combined FC-SDNN strategy effectively controls spurious oscillations in the proximity of discontinuities. Thanks to its use of a localized but smooth artificial viscosity term, whose support is restricted to a vicinity of flow-discontinuity points, the algorithm enjoys spectral accuracy and low dissipation away from flow discontinuities, and, in such regions, it produces smooth numerical solutions—as evidenced by an essential absence of spurious oscillations in level set lines. The FC-SDNN viscosity assignment, which does not require use of problem-dependent algorithmic parameters, induces a significantly lower overall dissipation than other methods, including the Fourier-spectral versions of the previous entropy viscosity method. The character of the proposed algorithm is illustrated with a variety of numerical results for the linear advection, Burgers and Euler equations in one and two-dimensional non-periodic spatial domains.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Bruno, Oscar P.0000-0001-8369-3014
Hesthaven, Jan S.0000-0001-8074-1586
Additional Information:© 2022 The Authors. Published by Elsevier Under a Creative Commons license - Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0). Received 29 October 2021, Revised 1 June 2022, Accepted 6 June 2022, Available online 9 June 2022, Version of Record 20 June 2022. OB and DL gratefully acknowledge support from NSF under contracts DMS-1714169 and DMS-2109831, from AFOSR under contract FA9550-21-1-0373, and from the NSSEFF Vannevar Bush Fellowship under ONR contract number N00014-16-1-2808. Initial conversations with J. Paul are also gratefully acknowledged. CRediT authorship contribution statement. Oscar P. Bruno: Conceptualization, Methodology, Validation, Investigation, Resources, Writing, Supervision, Funding acquisition. Jan Hesthaven: Conceptualization, Methodology, Investigation, Software, Resources. Daniel Leibovici: Conceptualization, Methodology, Software, Validation, Investigation, Writing, Visualization. The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)FA9550-21-1-0373
Vannever Bush Faculty FellowshipUNSPECIFIED
National Security Science and Engineering Faculty FellowshipN00014-16-1-2808
Subject Keywords:Machine learning; Neural networks; Shock dynamics; Artificial viscosity; Fourier continuation; Non-periodic domain
Record Number:CaltechAUTHORS:20220705-346684000
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Official Citation:Oscar P. Bruno, Jan S. Hesthaven, Daniel V. Leibovici, FC-based shock-dynamics solver with neural-network localized artificial-viscosity assignment, Journal of Computational Physics: X, Volume 15, 2022, 100110, ISSN 2590-0552,
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:115340
Deposited By: George Porter
Deposited On:08 Jul 2022 00:04
Last Modified:08 Jul 2022 00:04

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