A multigrid semi-implicit finite difference method for the two-dimensional shallow water equations

✍ Scribed by R. M. Spitaleri; L. Corinaldesi

• Publisher: John Wiley and Sons
• Year: 1997
• Tongue: English
• Weight: 248 KB
• Volume: 25
• Category: Article
• ISSN: 0271-2091
• DOI: 10.1002/(sici)1097-0363(19971215)25:11<1229::aid-fld593>3.0.co;2-m

✦ Synopsis

A multigrid semi-implicit ®nite difference method is presented to solve the two-dimensional shallow water equations which describe the behaviour of basin water under the in¯uence of the Coriolis force, atmospheric pressure gradients and tides. The semi-implicit ®nite difference method discretizes implicitly both the gradient of the water elevation in the momentum equations and the velocity divergence in the continuity equations and explicitly the convective terms using an Eulerian±Lagrangian approach. At each time step we apply the multigrid computation to solve the resulting linear, symmetric, pentadiagonal system of discrete equations. The multigrid algorithm, de®ned on staggered grids, provides accelerated convergence histories. We numerically simulate the water circulation in a closed rectangular basin, centrally crossed by a deeper channel. Moreover, simulation of the circulation in San Pablo Bay shows the high ¯exibility and applicability of this method to concrete problems. Visualizations of the computed variables, water depth and velocity, are shown by ®gures. Displays of convergence histories show promising multigrid acceleration.