On an open radiational boundary condition for weakly dispersive tsunami waves

Abstract

A radiational condition compatible with a weakly dispersive governing equation for tsunami waves is developed for use at the open lateral boundaries of a limited-domain propagation model. A Boussinesq-type governing equation for the interior is adopted. The resulting open boundary condition (OBC) is a modified Sommerfeld condition, in which the effects of weak dispersion, geometric spreading and shoaling are allowed. The OBC is applied along wave ray characteristics which intersect the open boundary obliquely. The numerical implementation employs Lagrange interpolations in two dimensions from information on a regular grid in the interior region. Test results indicate that the numerical boundary is highly transparent to incident waves in the absence of bottom topography. Weak dispersion effects (Airy dispersion, Poincaré dispersion and nonlinear dispersion) are faithfully reproduced in the test simulations. The effects of topography (reflection, refraction, and diffraction), which are not included in the OBC, result in some contamination of the solutions. However, the first few leading waves are free from serious error. Also the contamination due to topography near the open boundaries is sporadic and does not produce a cumulative effect. The modified OBC is shown to be a very significant improvement over the simple nondispersive Sommerfeld radiation condition.