The present investigation concerns optimum wave absorption
in numerical wave tanks. Recent developments have now established
that (i) absorption controllers based on Infinite Impulse
Response (IIR) filters are highly effective and (ii) cosh shaped
wave board geometries offer significant potential in terms of active
wave absorption due to their favourable added mass behaviour.
While (i) and (ii) have been shown individually, their
combination has never been demonstrated. To address this, a
cosh shaped wavemaker is implemented in a time-domain numerical
wave tank. Comparisons are presented between simple
proportional controllers and the IIR approach, where the latter
is demonstrated to offer excellent absorption performance over
a very broad range of incident wave conditions. In excess of
90% amplitude (or equivalently 99% energy) absorption is demonstrated
for the range 1 ≤ kh ≤ 8, where k is the wavenumber and
h is the water depth. A broad-banded absorption performance
of this type covers the vast majority of wave components present
in practical offshore wave spectra. Test cases are presented for
both regular and irregular seas, paving the way towards numerical
simulations of long random sea states. This paper focuses
on a two-dimensional description of the problem. The approach
adopted can also be extended to three dimensions, where reduced
domain sizes (no sponge layer requirements) offer orders of magnitude
improvement in terms of computational cost.