Stabilization of a time integrator for the 3D shallow water equations by smoothing techniques

A smoothing technique is applied to improve the stability of a semi-implicit time integrator for the three-dimensional shallow water equations. In this method the terms involving the vertical direction are treated implicitly. The stability condition on the time step depends only on the horizontal mesh sizes; therefore in the horizontal-direction a smoothing operator is added. Owing to the smoothing, the maximally stable time step increases considerably while the accuracy is hardly affected. Moreover, it turns out that the smoothing operator is efficient on vector and parallel computers.