Linear and nonlinear ultrasound simulations using the discontinuous Galerkin method

Document Type

Article

Publication Date

4-1-2018

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.

Identifier

85046075173 (Scopus)

Publication Title

Journal of the Acoustical Society of America

External Full Text Location

https://doi.org/10.1121/1.5032196

ISSN

00014966

PubMed ID

29716249

First Page

2438

Last Page

2448

Issue

4

Volume

143

Fund Ref

Focused Ultrasound Foundation

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