Stable, non-Reflective Condition of Perfectly Matched Layer in Computational Aeroacoustics

Abstract

In Computational Aeroacoustics, non-reflective boundary conditions such as radiation or absorbing boundary conditions are critical issues in that they can affect the whole solutions of computation. Among these types of boundary conditions, Perfectly Matched Layer boundary condition which has been widely used in Computational Electromagnetics and Computational Aeroacoustics is developed by augmenting the additional term by an absorption function in the original governing equations so as to stably absorb the outgoing waves. Even if Perfectly Matched Layer is perfectly non-reflective boundary condition analytically, spurious waves at the interface or instability could be shown since the analysis is performed in the discretized space. Hence, the study is focused on factors that affect these numerical instability and accuracy with particular numerical schemes. First, stability analysis preserving the dispersion relation is carried out in order to achieve the stability limit of time-step size. Then, through mathematical approach, stable absorption coefficient and PML width are suggested. In order to validate the prediction of analysis condition, numerical simulations are performed in generalized coordinate system as well as Cartesian coordinate system.