A comparison of a semi-implicit with an explicit scheme in a three-dimensional hydrodynamic model

Abstract

As the capacity of computers increases, the size and resolution of numerical models can be increased. In tidal models, however, using an explicit scheme together with high spatial resolution results in an unreasonably small time-step demanded by the CFL condition for stability. This condition is usually the most restrictive and applies to the propagation of the gravity wave.A fully nonlinear three-dimensional model has been developed, using the Galerkin method in the vertical dimension, in which the gravity wave terms are treated by an alternating-direction implicit scheme, while the friction, viscous and advective terms are treated explicitly. This permits a stable solution with a longer time-step than that required in an equivalent explicit scheme, while not needing as much computational effort as a fully implicit scheme. This semi-implicit model is compared with an explicit model in terms of efficiency, accuracy, and stability. Tidal and wind-driven flows and free oscillations in a rectangular sea model are examined, using various boundary conditions. The semi-implicit scheme takes approximately 1.1 times as long to run (per time-step) on the CRAY-1 computer as the explicit scheme.