186 1996 Charlotta Edlund lotta@tdb.uu.se A Solver for the Shallow-Water Equations on Overlapping Grids
Abstract
The two dimensional Shallow-Water Equations are solved on a complex geometry.
To achieve this we work with structured overlapping grids. The discretization
in space is done with centered second order finite differences. The time
integration is done with the Method of Lines, where we use a fourth order
Runge-Kutta method. The code is written in C++, using the object oriented
class library Overture.
The application for our solver is a simulation of the standing waves in
the Baltic Sea. We introduce a new way to handle the coast line. The points
along the coast line are identified and thereafter we make a least square
fitted spline through these points. The result is a smooth boundary curve.
We have applied our method to a number of different problems. For domains
with a flat bottom, no or very small artificial viscosity is required,
and the method is very robust. For irregular domains with bottom topography
artificial viscosity is required. If there are sharp gradients in the bottom
topography, the viscosity coefficient must be increased. In some cases
the solution becomes too smoothed by the strong viscosity. We have shown
that these difficulties disappear by simply removing the advection terms.
For our problems, characterized by small water velocity, the solution is
still accurate.