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Title: Treatment of the polar coordinate singularity in axisymmetric wave propagation using high-order summation-by-parts operators on a staggered grid

Abstract

In this paper, 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. 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 acoustic-gravity waves in a magmatic conduit.

Authors:
 [1];  [2];  [3];  [4]
  1. Stanford Univ., CA (United States). Dept. of Geophysics
  2. Stanford Univ., CA (United States). Dept. of Geophysics; Linköping Univ. (Sweden). Dept. of Mathematics. Division of Computational Mathematics
  3. Stanford Univ., CA (United States). Dept. of Geophysics. Inst. for Computational and Mathematical Engineering
  4. 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):
LLNL-JRNL-698320
Journal ID: ISSN 0045-7930
Grant/Contract Number:
AC52-07NA27344
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Computers and Fluids
Additional Journal Information:
Journal Volume: 149; Journal ID: ISSN 0045-7930
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; 42 ENGINEERING; polar coordinate singularity; summation-by-parts; high-order 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 high-order summation-by-parts 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 high-order summation-by-parts 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 high-order summation-by-parts 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 high-order summation-by-parts 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 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. 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 acoustic-gravity 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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