Accession Number : ADA115296

Title :   Relative Numerical Dispersion of Shallow Water Gravity Waves Caused by Three Differencing Techniques.

Descriptive Note : Technical note,

Corporate Author : NAVAL OCEAN RESEARCH AND DEVELOPMENT ACTIVITY NSTL STATION MS

Personal Author(s) : Harding,J M

PDF Url : ADA115296

Report Date : Apr 1982

Pagination or Media Count : 19

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)

Descriptors :   *Gravity waves, Shallow water, Water waves, Wave propagation, Mathematical models, Time, Velocity, Modification, Dispersing

Subject Categories : Physical and Dynamic Oceanography
      Hydrology, Limnology and Potamology
      Fluid Mechanics

Distribution Statement : APPROVED FOR PUBLIC RELEASE