Optimal Reduced Basis Method for Aeroacoustics with Impedance Boundary Conditions

Abstract

Solving the linearized Euler equations in the harmonic frequency domain amounts to solving a large linear system. Doing so repetitively can be costly, especially when some parameters need to be varied (for example, the acoustic impedance of a liner), such as in optimization and impedance eduction problems. To accelerate the calculations, the equations can first be projected onto a basis of reduced dimension, only requiring a limited number of full solutions called snapshots, which are calculated at different impedance values. This paper is concerned with finding an optimal set of impedances allowing the greedy creation of a reduced basis that leads to the most accurate surrogate modeling in the least number of calls to the direct solver. The optimal set of impedance values is first obtained on a two-dimensional duct configuration, and numerical verification tests are performed on a three-dimensional engine nacelle.