Efficient Implementation of Tam and Auriault'sTime-Domain Impedance Boundary Condition

Abstract

A new and efficient time-domain implementation is proposed for the impedance model originally introduced by Tam and Auriault (Tam, C. K. W., and Auriault, L., Time-Domain Impedance Boundary Conditions for Computational Aeroacoustics, AIAA Journal, Vol. 34, No. 5, May 1996, pp. 917-923). In the frequency domain, the pressure can be calculated from the product of the impedance with the normal velocity. In the time domain, a convolution is needed, which may become a costly operation. Present solutions for this problem involve either a full convolution and storage of a time history of data or a translation of the frequency-domain models to time-domain formulations involving time derivatives. The former approach is very costly in terms of memory and CPU time; the latter makes the implementation discretization specific and vulnerable to stability issues. A new formulation, based on recursive convolution, results in an efficient implementation that stores only one accumulator, which can be updated at each time step with minimal addition and multiplication. It allows for the exact representation of the impedance at a given frequency. The formulation is validated by a comparison with the measurement data from the NASA Langley Grazing Flow Impedance Tube. The simulations are performed by introducing a plane wave at a single frequency in the tube, and this is done for six frequencies and five different mean flow speeds.