Reduced Basis Method for the Convected Helmholtz Equation

TL;DR

This paper introduces a reduced basis method for efficiently solving the convected Helmholtz equation across multiple physical parameters, significantly reducing computational costs in aeroacoustic simulations.

Contribution

It develops an efficient a posteriori error estimator based on the primal norm and demonstrates its effectiveness through numerical experiments.

Findings

The reduced basis method accelerates solution computation for various parameters.

The proposed error estimator accurately predicts solution errors.

Numerical results confirm the efficiency and reliability of the approach.

Abstract

We present a reduced basis approach to solve the convected Helmholtz equation with several physical parameters. Physical parameters characterize the aeroacoustic wave propagation in terms of the wave and Mach numbers. We compute solutions for various combinations of parameters and spend a lot of time to figure out the desired set of parameters. The reduced basis method saves the computational effort by using the Galerkin projection, a posteriori error estimator, and greedy algorithm. Here, we propose an efficient a posteriori error estimator based on the primal norm. Numerical experiments demonstrate the good performance and effectivity of the proposed error estimator.