Three-dimensional benchmark problem for broadband time-domain impedance boundary conditions

The analytical solution of a three-dimensional initial and impedance boundary problem was derived and evaluated. The proposed problem can be used to benchmark broadband time-domain impedance boundary conditions in a three-dimensional context. The numerical solution using Tam and Auriault's broadband time-domain impedance boundary conditions very accurately reproduces the analytical solution. The outgoing and ingoing waves in free space with the same initial condition were determined in terms of the velocity potential.