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 language||English (US)|
|Number of pages||11|
|Journal||Journal of the Acoustical Society of America|
|State||Published - Apr 1 2018|
All Science Journal Classification (ASJC) codes
- Arts and Humanities (miscellaneous)
- Acoustics and Ultrasonics