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Linear and nonlinear ultrasound simulations using the discontinuous Galerkin method.

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Title: Linear and nonlinear ultrasound simulations using the discontinuous Galerkin method.
Authors: Kelly, James F.1 kellyja8@stt.msu.edu, Marras, Simone2, Zhao, Xiaofeng3, McGough, Robert J.3
Source: Journal of the Acoustical Society of America. Apr2018, Vol. 143 Issue 4, p2438-2448. 11p.
Subjects: Galerkin methods, Numerical analysis, Nonlinear wave equations, Wave equation, Dispersion (Chemistry)
Abstract: A nodal discontinuous Galerkin (DG) code based on the nonlinear wave equation is developed to simulate transient ultrasound propagation. The DG method has high-order accuracy, geometric flexibility, low dispersion error, and excellent scalability, so DG is an ideal choice for solving this problem. A nonlinear acoustic wave equation is written in a first-order flux form and discretized using nodal DG. A dynamic sub-grid scale stabilization method for reducing Gibbs oscillations in acoustic shock waves is then established. Linear and nonlinear numerical results from a two-dimensional axisymmetric DG code are presented and compared to numerical solutions obtained from linear and Khokhlov-Zabolotskaya-Kuznetsov-based simulations in FOCUS. The numerical results indicate that these nodal DG simulations capture nonlinearity, thermoviscous absorption, and diffraction for both flat and focused pistons in homogeneous media. [ABSTRACT FROM AUTHOR]
Copyright of Journal of the Acoustical Society of America is the property of American Institute of Physics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
An: 129388953
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PubTypeId: academicJournal
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  Data: Linear and nonlinear ultrasound simulations using the discontinuous Galerkin method.
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  Data: <searchLink fieldCode="AR" term="%22Kelly%2C+James+F%2E%22">Kelly, James F.</searchLink><relatesTo>1</relatesTo><i> kellyja8@stt.msu.edu</i><br /><searchLink fieldCode="AR" term="%22Marras%2C+Simone%22">Marras, Simone</searchLink><relatesTo>2</relatesTo><br /><searchLink fieldCode="AR" term="%22Zhao%2C+Xiaofeng%22">Zhao, Xiaofeng</searchLink><relatesTo>3</relatesTo><br /><searchLink fieldCode="AR" term="%22McGough%2C+Robert+J%2E%22">McGough, Robert J.</searchLink><relatesTo>3</relatesTo>
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+the+Acoustical+Society+of+America%22">Journal of the Acoustical Society of America</searchLink>. Apr2018, Vol. 143 Issue 4, p2438-2448. 11p.
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  Data: <searchLink fieldCode="DE" term="%22Galerkin+methods%22">Galerkin methods</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Nonlinear+wave+equations%22">Nonlinear wave equations</searchLink><br /><searchLink fieldCode="DE" term="%22Wave+equation%22">Wave equation</searchLink><br /><searchLink fieldCode="DE" term="%22Dispersion+%28Chemistry%29%22">Dispersion (Chemistry)</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: A nodal discontinuous Galerkin (DG) code based on the nonlinear wave equation is developed to simulate transient ultrasound propagation. The DG method has high-order accuracy, geometric flexibility, low dispersion error, and excellent scalability, so DG is an ideal choice for solving this problem. A nonlinear acoustic wave equation is written in a first-order flux form and discretized using nodal DG. A dynamic sub-grid scale stabilization method for reducing Gibbs oscillations in acoustic shock waves is then established. Linear and nonlinear numerical results from a two-dimensional axisymmetric DG code are presented and compared to numerical solutions obtained from linear and Khokhlov-Zabolotskaya-Kuznetsov-based simulations in FOCUS. The numerical results indicate that these nodal DG simulations capture nonlinearity, thermoviscous absorption, and diffraction for both flat and focused pistons in homogeneous media. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of the Acoustical Society of America is the property of American Institute of Physics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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      – Type: doi
        Value: 10.1121/1.5032196
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 11
        StartPage: 2438
    Subjects:
      – SubjectFull: Galerkin methods
        Type: general
      – SubjectFull: Numerical analysis
        Type: general
      – SubjectFull: Nonlinear wave equations
        Type: general
      – SubjectFull: Wave equation
        Type: general
      – SubjectFull: Dispersion (Chemistry)
        Type: general
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      – TitleFull: Linear and nonlinear ultrasound simulations using the discontinuous Galerkin method.
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            NameFull: Kelly, James F.
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            NameFull: Marras, Simone
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            NameFull: Zhao, Xiaofeng
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            NameFull: McGough, Robert J.
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          Dates:
            – D: 01
              M: 04
              Text: Apr2018
              Type: published
              Y: 2018
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              Value: 143
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            – TitleFull: Journal of the Acoustical Society of America
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