An Efficient Fgmres Solver for the Shallow Water Equations

The Shallow Water Equations (SWE) are a set of nonlinear hyperbolic equations, describing long waves relative to the water depth. Physical phenomena such as tidal waves in rivers and seas, breaking of waves on shallow beaches and even harbour oscillations can be modelled successfully with the SWE. The 3D SWE (1.1){(1.3) given below for Cartesian (;) coordinates are based on the hydrostatic assumption, that the innuence of the vertical component of the acceleration of the water particles on the pressure can be neglected. (1.3) We denote by the water elevation above some plane of reference, hence the total water depth is given by H = d + , where d is the depth below this plane of reference. The scaled vertical coordinate = z ? d + varies between ?1 at the bottom and 0 at the free surface. The velocities in the-and-directions are denoted by u and v respectively, while ! represents the transformed vertical velocity. The parameter f accounts for the Coriolis force due to the rotation of the Earth. The viscosity is modelled using H and V. In each-plane H models the \horizontal" viscosity, while V describes the viscosity in the vertical () direction.