A model order reduction technique for the linearised compressible flow equations

Abstract

Viscous effects in acoustics are significant if the thickness of the oscillating viscous boundary layer (Stokes boundary layer) becomes comparable to characteristic problem dimensions. For air as an acoustic medium, this is frequently the case in small‐scale devices like micro‐electro‐mechanical systems or micro‐perforated panels for sound absorption. Accurate modelling of viscous effects can be done by the solution of the linearised compressible flow equations by the finite element method, which is computationally demanding due to the high number of unknowns arising in the problem: pressure, velocity and temperature. Furthermore, the discretisation must resolve the thin viscous boundary layers, creating a model with a high number of degrees of freedom. We suggest a projection‐based model order reduction procedure using the system eigenmodes as generalised coordinates. The procedure is tested based on a simple example problem in 2D. Here we show that the derived reduced order model is accurate and computationally highly efficient. The number of degrees of freedom can be reduced by several orders of magnitude, from around 30 000 to 100, thereby dramatically reducing the computation time for harmonic solutions.