Acoustic vibration problem for dissipative fluids

TL;DR

This paper develops and analyzes a finite element method for solving the acoustic vibration problem in dissipative fluids, providing spectral characterization, proving convergence, and demonstrating effectiveness through numerical tests.

Contribution

It introduces a Raviart-Thomas finite element approach for a quadratic eigenvalue problem related to dissipative fluids, ensuring no spurious modes and optimal convergence.

Findings

Method is free of spurious modes

Achieves optimal convergence order

Numerical tests confirm effectiveness

Abstract

In this paper we analyze a finite element method for solving a quadratic eigenvalue problem derived from the acoustic vibration problem for a heterogeneous dissipative fluid. The problem is shown to be equivalent to the spectral problem for a noncompact operator and athorough spectral characterization is given. The numerical discretization of the problem is based on Raviart-Thomas finite elements. The method is proved to be free of spurious modes and to converge with optimal order. Finally, we report numerical tests which allow us to assess the performance of the method.