Earth System Physics Seminar

[Pandora Malchose Pieri]

EARTH SYSTEM PHYSICS SEMINAR

Friday, 22 September 2006
11:00 hrs, MB SEMINAR ROOM

Magdi M. SHOUCRI
Institut de recherche d'Hydro-Quebec
Varennes, Quebec
Canada

"THE APPLICATION OF A FRACTIONAL STEP METHOD FOR THE NUMERICAL SOLUTION 
OF THE SHALLOW WATER EQUATIONS"

Abstract:
A fractional step technique is applied for the numerical solution of 
the shallow water equations. The height and velocity field of the 
shallow water equations are discretized on a fixed Eulerian grid and 
time-stepped with a fractional step method, where the Riemann 
invariants of the equations are interpolated at each time step along 
the characteristics using a cubic spline interpolation. The method has 
the great advantage of solving the shallow water equations without the 
iterative steps involved in the multi-dimensional interpolation 
problems, and without the iteration associated with the intermediate 
step of solving the Helmholtz equation. The absence of iterative steps 
in the present technique makes it very suitable for problems in which 
small time steps and grid sizes are required (as in regional climate 
modeling), and the simplicity of the method makes it suitable to 
parallel computer. We present results obtained by solving the 2D 
barotropic model. We present also results obtained for the calculation 
of the potential vorticity field of a zonal jet, which develops steep 
gradients and evolve into thin filaments during the evolution, and 
which is nicely calculated at every time step from the solution of the 
code. Finally an application for the solution of the equations 
pertinent to El Nino variability in oceanography will be outlined.