Linear and nonlinear ultrasound simulations using the discontinuous Galerkin method

James F. Kelly, Simone Marras, Xiaofeng Zhao, Robert J. McGough

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)2438-2448
Number of pages11
JournalJournal of the Acoustical Society of America
Issue number4
StatePublished - Apr 1 2018

All Science Journal Classification (ASJC) codes

  • Arts and Humanities (miscellaneous)
  • Acoustics and Ultrasonics


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