RADIATION BOUNDARY-CONDITIONS FOR DISPERSIVE WAVES

The author develops radiation boundary conditions for the numerical mo deling of dispersive waves. During the construction of such boundary c onditions, the goal is to simulate the outward radiation of waves near an artificial computational boundary. The velocities of the outgoing waves are typically involved in processes of this nature. A central pr oblem in the dispersive case is that two different types of velocities are present, phase velocity and group velocity, and each can vary wit h wavenumber and frequency. With the boundary conditions developed in this paper, the user needs to specify some parameters; in the cases th at are emphasized here, the parameters can be interpreted in terms of phase velocities of waves that are absorbed exactly at the computation al boundary. The amount of reflected error is a continuous function of the parameters, and the performance of the boundary conditions is not sensitive to the choice of parameters. Good performance is obtained i n numerical tests involving data that have broad bands in wavenumber s pace. The formulas for boundary conditions are based on compositions o f simple first-order differential operators; the same formulas can be applied without modification to problems in both one and several dimen sions.