Absorbing-Generating Boundary Condition for Shallow Water Models

An absorbing-generating boundary condition is derived for the two-dimensional-horizontal nonlinear shallow equations using the method of characteristics. It assumes local superposition of the incoming and outgoing long waves at the boundary, and uses a relationship between the flux and surface elevation of the waves. This boundary condition allows the outgoing waves to leave the computational domain through the boundaries with a minimum of reflection, while specifying incoming waves at the same boundaries. The boundary condition's absorbing properties are tested for both linear and nonlinear waves for a range of amplitudes and of angles of incidence. Its performance is compared to the classical Sommerfeld radiation condition for the linear case and is shown to cause significantly less reflection errors, especially for oblique angles. Also, a case of simultaneous absorption and generation of waves at the same boundary is analyzed where it is shown that the errors are of the same order as for the case of absorption only. Finally, the boundary condition is extended to include known currents.