A discontinuous Galerkin coupling for nonlinear elasto-acoustics. (25th November 2021)

• Record Type: Journal Article
• Authors: Muhr, Markus; Wohlmuth, Barbara; Nikolić, Vanja
• Is Part Of: IMA journal of numerical analysis. Volume 43:Number 1(2023)
• Page Start: 225
• Page End: 257
• Publication Date: 2021-11-25
• Subjects: nonlinear acoustics -- elasto-acoustic coupling -- discontinuous Galerkin methods -- Westervelt's equation -- Kuznetsov's equation -- ultrasonic waves; Numerical analysis -- Periodicals; 519.405
• DOI: 10.1093/imanum/drab089
• Languages: English
• ISSNs: 0272-4979

Abstract

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.