Relative numerical dispersion of shallow water gravity waves caused by three difference techniques
Abstract
Using analytical and numerical techniques we compare the effect of three different timedifferencing methods on the propagation of shallowwater gravity waves. We compare the numerical dispersion of both phase and group velocities caused by a centeredintime explicit formulation, a centeredintime implicit method, and a trapezoidalintime implicit treatment. All three techniques slow the waves relative to their theoretical phase and group velocities. For each method, the slowing increases with decreasing spatial resolution and with decreasing temporal resolution. For delta t square root of gh/d < or = 1, the slowing increases as we switch from explicit, to trapezoidal implicit, to centered implicit methods. In this formula, square root of gh = theoretical shallow water gravity wave speed, delta t = time increment, and d = smallest space increment between like variable grid points. For delta t square root of gh/d > 1, the trapezoidal implicit scheme again outperforms the centered implicit scheme.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 April 1982
 Bibcode:
 1982STIN...8230510H
 Keywords:

 Dispersing;
 Gravity Waves;
 Mathematical Models;
 Shallow Water;
 Surface Waves;
 Wave Propagation;
 Computerized Simulation;
 Gravitational Waves;
 Group Velocity;
 Phase Velocity;
 Water Waves;
 Fluid Mechanics and Heat Transfer