Application of the Time-Explicit Nodal Discontinuous Galerkin Method to Modeling of Nonlinear Ultrasound Propagation in Inhomogeneous Media
Nonlinear acoustic phenomena play an essential role in many biomedical applications, such as high intensity focused ultrasound (HIFU) for thermal ablation of tumors, ultrasonic imaging, shock-wave lithotripsy, etc. The efficient numerical modeling of nonlinear ultrasound usually requires large computational resources, due to the necessity to resolve higher-order harmonics and/or shocks developed during the propagation of a finite amplitude ultrasonic signal over a distance of many fundamental wavelengths.In this work, we propose a numerical scheme based on the time-explicit higher order nodal discontinuous Galerkin finite element method (dG-FEM). The method is known as an efficient tool for solving transient acoustically large problems at low computational costs. Its main advantages are low memory consumption, great scalability, and ability to operate on unstructured and nonconforming meshes, which makes it possible to use this method on both clusters and common workstations.The proposed approach is applied to solving a coupled nonlinear acoustic/linear elastic first-order hyperbolic system. The propagation of the signal through an inhomogeneous medium is treated by proper upwind numerical fluxes imposed on the interfaces between the domains with different acoustic and elastic properties.