Numerical Analysis of Time-Dependent Galbrun Equation in an Infinite Duct

TL;DR

This paper develops a mathematical and numerical framework for analyzing the time-dependent Galbrun equation in a duct, focusing on regularized formulations and finite element methods for acoustic flow modeling.

Contribution

It introduces a regularized variational formulation for the Galbrun equation in a duct and proposes absorbing boundary conditions suitable for finite element approximation.

Findings

Validates the regularized formulation for sub-sonic flows

Provides a finite element approach for numerical simulation

Establishes absorbing boundary conditions for accurate modeling

Abstract

In this paper we are interested in the mathematical and numerical analysis of the time-dependent Galbrun equa- tion in a rigid duct. This equation models the acoustic propagation in presence of flow [1]. We propose a regu- larized variational formulation of the problem, in the sub- sonic case, suitable for an approximation by Lagrange finite elements, and corresponding absorbing boundary conditions.