Ar. Vandongeren et Ia. Svendsen, ABSORBING-GENERATING BOUNDARY-CONDITION FOR SHALLOW-WATER MODELS, Journal of waterway, port, coastal, and ocean engineering, 123(6), 1997, pp. 303-313
An absorbing-generating boundary condition is derived for the two-dime
nsional-horizontal nonlinear shallow equations using the method of cha
racteristics. It assumes local superposition of the incoming and outgo
ing long waves at the boundary, and uses a relationship between the fl
ux and surface elevation of the waves. This boundary condition allows
the outgoing waves to leave the computational domain through the bound
aries with a minimum of reflection, while specifying incoming waves at
the same boundaries. The boundary condition's absorbing properties ar
e tested for both linear and nonlinear waves for a range of amplitudes
and of angles of incidence. Its performance is compared to the classi
cal Sommerfeld radiation condition for the linear case and is shown to
cause significantly less reflection errors, especially for oblique an
gles. 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 bou
ndary condition is extended to include known currents.