Consequences of Inaccuracies in Open Boundary Conditions of Numerical Models
by
Robert A. Pearson
UNSW

An artificial boundary condition that allows waves to pass from a limited computational domain is the Sommerfeld Radiation Boundary Condition. A simple analytical examination of this equation suggests that if the phase speed of the wave arriving at the boundary is not that used in the formulation the wave should be partially reflected, with some energy leaving the domain. A simple numerical model which admits dispersive waves is used to demonstrate the behaviour of this boundary condition. As anticipated when the estimate is correct the solution from the limited area model behaves as that of a larger domain. The emphasis in this paper is on the model results when the estimate of the phase speed is incorrect. The numerical experiments indicate that in general an overestimate of the phase is preferable to an underestimate. However with an overestimate of the phase and at some time periods the energy inside the area of interest can be larger that that of the same model with a rigid boundary.

The balance between the available and kinetic energies inside the domain is also different for the overestimate of the phase than the underestimate. The relative phase of the wave is reversed. These general properties occur throughout a variety of values of the available physical parameters. A plausible explanation for this phenomena is given. For this model it is demonstrated that some existing techniques that give and estimate of the phase speed from the solution itself give very inaccurate results.

Date received: July 25, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cadk-47.