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.