A set of Boussinesq-type equations with improved linear frequency disp
ersion in deeper water is solved numerically using a fourth order accu
rate predictor-corrector method. The model can be used to simulate the
evolution of relatively long, weakly nonlinear waves in water of cons
tant or variable depth provided the bed slope is of the same order of
magnitude as the frequency dispersion parameter. By performing a linea
rized stability analysis, the phase and amplitude portraits of the num
erical schemes are quantified, providing important information on prac
tical grid resolutions in time and space. In contrast to previous mode
ls of the same kind, the incident wave field is generated inside the f
luid domain by considering the scattered wave field in one part of the
fluid domain and the total wave field in the other. Consequently, wav
es leaving the fluid domain are absorbed almost perfectly in the bound
ary regions by employment of damping terms in the mass and momentum eq
uations. Additionally, the form of the incident regular wave field is
computed by a Fourier approximation method which satisfies the governi
ng equations accurately in water of constant depth. Since the Fourier
approximation method requires an Eulerian mean current below wave trou
gh level or a net mass transport velocity to be specified, the method
can be used to study the interaction of waves and currents in closed a
s well as open basins. Several computational examples are given. These
illustrate the potential of the wave generation method and the capabi
lity of the developed model. (C) 1998 Elsevier Science Ltd. All rights
reserved.