X-Beach : Processes and model formulation

Domain and definitions

Coordinate system

XBeach uses a coordinate system where the computational x-axis is always oriented towards the coast, approximately perpendicular to the coastline, and the y-axis is alongshore, see Figure A.1 and Figure A.1. This coordinate system is defined in world coordinates. The grid size in x- and y-direction may be variable but the grid must be curvilinear. Alternatively, in case of a rectangular grid (a special case of a curvilinear grid) the user can provide coordinates in a local coordinate system that is oriented with respect to world coordinates (xw, yw) through an origin (xori, yori) and an orientation (alfa) as depicted in Figure A.1. The orientation is defined counter-clockwise w.r.t. the xw-axis (East).

Grid set-up

The grid applied is a staggered grid, where the bed levels, water levels, water depths and concentrations are defined in cell centers, and velocities and sediment transports are defined in u- and v-points, viz. at the cell interfaces. In the wave energy balance, the energy, roller energy and radiation stress are defined at the cell centers, whereas the radiation stress gradients are defined at u- and v-points.

Velocities at the u- and v-points are denoted by the output variables uu and vv respectively; velocities u and v at the cell centers are obtained by interpolation and are for output purpose only. The water level, zs, and the bed level, zb, are both defined positive upward. uv and vu are the u-velocity at the v-grid point and the v-velocity at the u-grid point respectively. These are obtained by interpolation of the values of the velocities at the four surrounding grid points. 

The model solves coupled 2D horizontal equations for wave propagation, flow, sediment transport and bottom changes, for varying (spectral) wave and flow boundary conditions.