An efficient numerical model for wave refraction, diffraction and reflectio
n is presented in this paper. In the model the modified time-dependent mild
-slope equation is transformed into an evolution equation and an improved A
DI method involving a relaxation factor is adopted to solve it. The method
has the advantage of improving the numerical stability and convergence rate
by properly determining the relaxation factor. The range of the relaxation
factor making the differential scheme unconditionally stable is determined
by stability analysis. Several verifications are performed to examine the
accuracy of the present model. The numerical results coincide with the anal
ytic solutions or experimental data very well and the computer time is redu
ced.