Treatment of the polar coordinate singularity in axisymmetric wave propagation using highorder summationbyparts operators on a staggered grid
Abstract
In this paper, we develop a highorder finite difference scheme for axisymmetric wave propagation in a cylindrical conduit filled with a viscous fluid. The scheme is provably stable, and overcomes the difficulty of the polar coordinate singularity in the radial component of the diffusion operator. The finite difference approximation satisfies the principle of summationbyparts (SBP), which is used to establish stability using the energy method. To treat the coordinate singularity without losing the SBP property of the scheme, a staggered grid is introduced and quadrature rules with weights set to zero at the endpoints are considered. Finally, the accuracy of the scheme is studied both for a model problem with periodic boundary conditions at the ends of the conduit and its practical utility is demonstrated by modeling acousticgravity waves in a magmatic conduit.
 Authors:
 Stanford Univ., CA (United States). Dept. of Geophysics
 Stanford Univ., CA (United States). Dept. of Geophysics; Linköping Univ. (Sweden). Dept. of Mathematics. Division of Computational Mathematics
 Stanford Univ., CA (United States). Dept. of Geophysics. Inst. for Computational and Mathematical Engineering
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing
 Publication Date:
 Research Org.:
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Stanford Univ., CA (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1438664
 Alternate Identifier(s):
 OSTI ID: 1396504
 Report Number(s):
 LLNLJRNL698320
Journal ID: ISSN 00457930
 Grant/Contract Number:
 AC5207NA27344
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Computers and Fluids
 Additional Journal Information:
 Journal Volume: 149; Journal ID: ISSN 00457930
 Publisher:
 Elsevier
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; 42 ENGINEERING; polar coordinate singularity; summationbyparts; highorder finite difference method; staggered grid; axisymmetric wave propagation
Citation Formats
Prochnow, Bo, O'Reilly, Ossian, Dunham, Eric M., and Petersson, N. Anders. Treatment of the polar coordinate singularity in axisymmetric wave propagation using highorder summationbyparts operators on a staggered grid. United States: N. p., 2017.
Web. doi:10.1016/j.compfluid.2017.03.015.
Prochnow, Bo, O'Reilly, Ossian, Dunham, Eric M., & Petersson, N. Anders. Treatment of the polar coordinate singularity in axisymmetric wave propagation using highorder summationbyparts operators on a staggered grid. United States. doi:10.1016/j.compfluid.2017.03.015.
Prochnow, Bo, O'Reilly, Ossian, Dunham, Eric M., and Petersson, N. Anders. Thu .
"Treatment of the polar coordinate singularity in axisymmetric wave propagation using highorder summationbyparts operators on a staggered grid". United States.
doi:10.1016/j.compfluid.2017.03.015. https://www.osti.gov/servlets/purl/1438664.
@article{osti_1438664,
title = {Treatment of the polar coordinate singularity in axisymmetric wave propagation using highorder summationbyparts operators on a staggered grid},
author = {Prochnow, Bo and O'Reilly, Ossian and Dunham, Eric M. and Petersson, N. Anders},
abstractNote = {In this paper, we develop a highorder finite difference scheme for axisymmetric wave propagation in a cylindrical conduit filled with a viscous fluid. The scheme is provably stable, and overcomes the difficulty of the polar coordinate singularity in the radial component of the diffusion operator. The finite difference approximation satisfies the principle of summationbyparts (SBP), which is used to establish stability using the energy method. To treat the coordinate singularity without losing the SBP property of the scheme, a staggered grid is introduced and quadrature rules with weights set to zero at the endpoints are considered. Finally, the accuracy of the scheme is studied both for a model problem with periodic boundary conditions at the ends of the conduit and its practical utility is demonstrated by modeling acousticgravity waves in a magmatic conduit.},
doi = {10.1016/j.compfluid.2017.03.015},
journal = {Computers and Fluids},
number = ,
volume = 149,
place = {United States},
year = {Thu Mar 16 00:00:00 EDT 2017},
month = {Thu Mar 16 00:00:00 EDT 2017}
}
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