A discontinuous Galerkin coupling for nonlinear elasto-acoustics

TL;DR

This paper develops a finite element discontinuous Galerkin method for nonlinear elasto-acoustic problems with material jumps, providing convergence analysis and numerical validation in 3D medical ultrasound applications.

Contribution

It introduces a novel coupling approach combining discontinuous Galerkin methods with interface conditions for nonlinear elasto-acoustic problems involving material heterogeneities.

Findings

Convergence rates are established for the finite element approximation.

Numerical simulations confirm theoretical results and compare elastic and acoustic tissue models.

The method effectively handles material discontinuities in 3D simulations.

Abstract

Inspired by medical applications of high-intensity ultrasound, we study a coupled elasto-acoustic problem with general acoustic nonlinearities of quadratic type as they arise, for example, in the Westervelt and Kuznetsov equations of nonlinear acoustics. We derive convergence rates in the energy norm of a finite element approximation to the coupled problem in a setting that involves different acoustic materials and hence jumps within material parameters. A subdomain-based discontinuous Galerkin approach realizes the acoustic-acoustic coupling of different materials. At the same time, elasto-acoustic interface conditions are used for a mutual exchange of forces between the different models. Numerical simulations back up the theoretical findings in a three-dimensional setting with academic test cases as well as in an application-oriented simulation, where the modeling of human tissue as an elastic versus an acoustic medium is compared.