This paper presents a numerical scheme of arbitrary order of accuracy in both space and time, based on the arbitrary high-order derivatives methodology, for transient acoustic simulations. The scheme combines the nodal discontinuous Galerkin method for the spatial discretization and the Taylor series integrator (TSI) for the time integration. The main idea of the TSI is a temporal Taylor series expansion of all unknown acoustic variables in which the time derivatives are replaced by spatial derivatives via the Cauchy-Kovalewski procedure. The computational cost for the time integration is linearly proportional to the order of accuracy. To increase the computational efficiency for simulations involving strongly varying mesh sizes or material properties, a local time-stepping (LTS) algorithm accompanying the arbitrary high-order derivatives discontinuous Galerkin (ADER-DG) scheme, which ensures correct communications between domains with different time step sizes, is proposed. A numerical stability analysis in terms of the maximum allowable time step sizes is performed. Based on numerical convergence analysis, we demonstrate that for nonuniform meshes, a consistent high-order accuracy in space and time is achieved using ADER-DG with LTS. An application to the sound propagation across a transmissive noise barrier validates the potential of the proposed method for practical problems demanding high accuracy.
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An arbitrary high-order discontinuous Galerkin method with local time-stepping for linear acoustic wave propagation
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January 2021
January 25 2021
An arbitrary high-order discontinuous Galerkin method with local time-stepping for linear acoustic wave propagation
Huiqing Wang
;
Huiqing Wang
a)
Building Physics and Services, Department of the Built Environment, Eindhoven University of Technology
, P.O. Box 513, Eindhoven, 5600 MB, The Netherlands
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Matthias Cosnefroy;
Matthias Cosnefroy
Building Physics and Services, Department of the Built Environment, Eindhoven University of Technology
, P.O. Box 513, Eindhoven, 5600 MB, The Netherlands
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Maarten Hornikx
Maarten Hornikx
b)
Building Physics and Services, Department of the Built Environment, Eindhoven University of Technology
, P.O. Box 513, Eindhoven, 5600 MB, The Netherlands
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a)
Electronic mail: h.wang6@tue.nl, ORCID: 0000-0003-3465-3555.
b)
ORCID: 0000-0002-8343-6613.
J. Acoust. Soc. Am. 149, 569–580 (2021)
Article history
Received:
October 02 2020
Accepted:
December 21 2020
Citation
Huiqing Wang, Matthias Cosnefroy, Maarten Hornikx; An arbitrary high-order discontinuous Galerkin method with local time-stepping for linear acoustic wave propagation. J. Acoust. Soc. Am. 1 January 2021; 149 (1): 569–580. https://doi.org/10.1121/10.0003340
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