Relative Numerical Dispersion of Shallow Water Gravity Waves Caused by Three Differencing Techniques.
Abstract
Using analytical and numerical techniques we compare the effect of three different time-differencing methods on the propagation of shallow-water gravity waves. We compare the numerical dispersion of both phase and group velocities caused by a centered-in-time explicit formulation, a centered-in-time implicit method, and a trapezoidal-in-time 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. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 01, 1982
- Accession Number
- ADA115296
Entities
People
- J. M. Harding