Modeling of the seat dip effect using the finite-difference time-domain method

In this paper the use of the finite-difference time-domain technique for the modeling of the seat dip effect in concert halls is demonstrated. The linear time-domain acoustic partial differential equations are discretized using a finite-difference technique. The second-order accurate differencing scheme is time–space centered, and the velocity and pressure are solved on an interlaced mesh. First- and second-order Mur absorbing boundary conditions, originally formulated for electromagnetic problems, are adapted to the acoustics case and used to truncate the numerical grid. The technique is first verified by comparing the numerical results to the analytic solution of a simple point source. Results from computer simulations of the seat dip phenomena are compared with the findings of previous studies where measurements had been made on scale models and in real concert halls. The computer model successfully predicts the effects associated with the source–receiver distance, the height of the receiver, and the height of the source.