A review of time domain impedance boundary conditions

Christoph Richter

Over the last 15 years, time domain impedance boundary conditions have been investigated by various authors. In a review, a general framework of time domain impedance boundary conditions is presented and then filled with a set of outstanding mathematical and numerical methods from literature. All of the authors struggled with an instability with grazing flow. Mainly this is linked to the Ingard or Myers model of the sound propagation through a sheared flow. This is reviewed in a broader context including possible applications of impedance boundary conditions (i.e. turbomachinery noise and noise absorber optimization) into this discussion. Stable solutions are presented, that go from simple workarounds which are based on the wave number characteristics of the instability to a completely different modeling of the physics. At one end of the scale are seemingly trivial ideas, as the use of the Ingard/Myers boundary condition on a coarser mesh or a fully resolved flow profile; and at the other end high fidelity DNS simulations of single cells and holes under gazing flow conditions is put the whole idea of macroscopic impedance on test. It is shown, that each solutions has its advantages for some applications and may be infeasible in other cases.

Mots clés: CAA; Time doamin Impedance; propagation; duct acoustics

Domaines: Acoustique [physics.class-ph]

Christoph Richter. A review of time domain impedance boundary conditions. Acoustics 2012, Apr 2012, Nantes, France. ⟨hal-00810672⟩