Application and Verification of Broadband Time Domain Impedance Boundary Conditions in Multi-Dimensional Acoustic Problems

Abstract

Broadband time domain impedance boundary conditions are implemented in multi-dimensional acoustic problems. A series of acoustic wave propagation problems in one, two and three-dimensions with an impedance boundary are then solved as test cases both analytically and numerically. The numerical results of all the three acoustic problems agree very well with those of the analytical solutions. To the authors' knowledge, it is the first time that the analytical solution to the three-dimensional problem of this kind is derived analytically. The impedance boundary condition is also tested against the single frequency time domain boundary condition to gain further confidence. Finally, it is demonstrated that the impedance boundary condition is stable under both uniform and sheared mean flow conditions with other test cases.