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Treatment of the polar coordinate singularity in axisymmetric wave propagation using high-order summation-by-parts operators on a staggered grid
Stanford University, CA 94305 USA.
Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering. Stanford University, CA 94305 USA.
Stanford University, CA 94305 USA.
Lawrence Livermore National Lab, CA 94551 USA.
2017 (English)In: Computers & Fluids, ISSN 0045-7930, E-ISSN 1879-0747, Vol. 149, 138-149 p.Article in journal (Refereed) Published
Abstract [en]

We develop a high-order 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 summation-by-parts (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. 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 acoustic-gravity waves in a magmatic conduit. (C) 2017 Elsevier Ltd. All rights reserved.

Place, publisher, year, edition, pages
PERGAMON-ELSEVIER SCIENCE LTD , 2017. Vol. 149, 138-149 p.
Keyword [en]
Polar coordinate singularity; Summation-by-parts; High-order finite difference method; Staggered grid; Axisymmetric wave propagation
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-137585DOI: 10.1016/j.compfluid.2017.03.015ISI: 000400038700010OAI: oai:DiVA.org:liu-137585DiVA: diva2:1097521
Note

Funding Agencies|Chevron fellowship

Available from: 2017-05-22 Created: 2017-05-22 Last updated: 2017-05-22

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CiteExportLink to record
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Citation style
  • apa
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