Totallyimplicit integration of a limitedarea grid point model of the shallowwater equations
Abstract
Implicit time difference schemes were sequentially applied to the nonlinear shallow water equations on a limited area fine mesh domain, employing semimomentum space differencing. Consistent, well posed boundary conditions were accurately imposed on the finite difference approximation. Energy integral invariants of the model were found to be conserved by the finite difference approximation for 72 hour forecasts. The systems of nonlinear algebraic equations resulting from the finite difference discretization were solved by a linearized iterative procedure. Operator control of the time step allowed the truncation error to be restricted to a prescribed limit. Numerical integration was performed with time steps five times as large as the greatest allowed for by the Courant, Friedrichs and Levy (C.F.L.) criterion for explicit time schemes.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 August 1976
 Bibcode:
 1976STIN...7724429N
 Keywords:

 Finite Difference Theory;
 Numerical Integration;
 Shallow Water;
 Approximation;
 Barotropic Flow;
 Coordinates;
 Forecasting;
 Gravity Waves;
 Iteration;
 Nonlinear Equations;
 Fluid Mechanics and Heat Transfer