Improved boundary equations for elliptic water wave models

Approximate equations for the elliptic mild slope equation are derived based on Padé approximation and used as absorbing boundaries. The new boundary equations can absorb the incident waves for high range of wave incidence angle. In addition, the new boundary equations can be used iteratively to refine the solution by eliminating reflections from the boundaries. An iterative conjugate gradient scheme has been used to solve the elliptic water wave equation and the new boundary equations. The model developed can accommodate for wave diffraction, refraction and reflections from structures with wide range of wave angles at the boundaries. The new model has been tested for several cases. The model compares very well with other models.