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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]
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Database: Engineering Source
Description
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]
ISSN:00014966
DOI:10.1121/1.5032196