Reduced-order transient simulations of the convected wave equation with perfectly matched layers

Abstract

Perfectly matched layers (PMLs) have been widely employed to create non reflecting boundary conditions for various wave-propagation problems. Stability and efficiency are crucial for transient simulations of such systems. For wave propagation with flow, classical PMLs can suffer from stability issues. Although recent improvements address these concerns, we found they are inaccurate at low frequencies. In addition, PMLs require a sufficient number of layers to reduce numerical errors and result in additional variables in the time domain, leading to a high computational cost for transient simulations. This paper presents a novel reduced-order approach to enable fast, stable, and accurate transient simulations of the convected wave equation with PMLs. Firstly, the convected Helmholtz equation is transformed into a modified Helmholtz equation using the Lorentz transformation. The employment of PMLs in the Lorentz space guarantees stability and accuracy. Secondly, auxiliary variables are designed to build the time-domain model, where the stable model order reduction can be applied to accelerate the transient simulations. The proposed method is successfully verified by numerical experiments.

More information

Identifiers

ORCID for Sjoerd Van Ophem: orcid.org/0000-0003-1050-7318

Catalogue record

Export record

Altmetrics