Validation of a time domain impedance formulation for the case of a 2D rectangular lined duct with a non-uniform mean-flow with a finite boundary layer thickness

A validation and improvement of a recently developed time domain impedance formulation based on recursive convolution has been carried out. This formulation has been implemented using an in-house time-domain Runge-Kutta Discontinous Galerkin (RKDG) Linearized Euler Equations (LEE) solver. At first, a validation has been carried out on a 2D lined rectangular duct both without flow and with uniform mean flow. The RKDG results have been compared with the analytical reference solutions for the problem under consideration. In a second stage the case of the 2D rectangular lined duct with a non-uniform mean flow is validated to include the effect of a finite boundary layer thickness on the acoustic damping properties.