Backscattering in complex flows: application of the One-Way Euler equations to Poiseuille flow inside lined duct

Abstract

We present an improved formulation of the numerical One-Way approximation that permits to diagonalize in a fully numerical way the propagation operator of a general hyperbolic system. In this paper, it is applied to the linearized Euler equations in the case of a duct with a partially lined section presenting a Poiseuille flow. Domain decomposition is developed in this paper since it is needed for the handling of the transverse boundary conditions discontinuity (hard-wall and impedance condition) which is at the origin of the refraction and reflection of the incident wave inside the computational domain. The results of the One-Way method are compared to experimental and numerical results and show a good accuracy for a low amount of computing resources.

Domain decomposition method based on One-Way approaches for sound propagation in a partially lined duct

“…However, this method is limited by a hypothesis of slow variation in the baseflow along the propagation direction, which includes also any variation in the transverse boundary conditions. A derivation of these One-Way equations has been presented in [20] and applied to the problem of a partially lined duct in [21]. This method is based on the full numerical construction of the projection operators that are needed to take into account the reflection and transmission of waves across any variation.…”