Work

Asymptotic-preserving hybridizable discontinuous Galerkin method for the Westervelt quasilinear wave equation

Year: 2024

Type: article

Abstract: We discuss the asymptotic-preserving properties of a hybridizable discontinuous Galerkin method for the Westervelt model of ultrasound waves. More precisely, we show that the proposed method is robust with respect to small values of the sound diffusivity damping parameter δ by deriving low- and high-order energy stability estimates, and a priori error bounds that are independent of δ . Such bounds are then used to show that, when δ → 0 + , the method remains stable and the discrete acoustic velocity potential ψ h ( δ ) converges to ψ h ( 0 ) , where the latter is the singular vanishing dissipation limit. Moreover, we prove optimal convergence rates for the approximation of the acoustic particle velocity variable υ =∇ ψ . The established theoretical results are illustrated with some numerical experiments.

Source: ESAIM Mathematical Modelling and Numerical Analysis

DOI: 10.1051/m2an/2024085

Authors: Sergio Gómez, Mostafa Meliani

Institutions: University of Milano-Bicocca, Radboud University Nijmegen, Czech Academy of Sciences, Czech Academy of Sciences, Institute of Mathematics

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: