A new model for wave transformation around axis-symmetric islands without vertical wall along the coastline

•A numerical solution of the mild-slope equation is suggested for wave transformation.•The water depth becomes zero at the coastline and varies in the radial direction.•The boundary condition at the coastline is satisfied by applying an analytical solution.•The barrier effects on the wave transformation are investigated.

In this study, we develop a numerical model using the elliptic mild-slope equation for waves propagating around axis-symmetric topographies where the water depth varies arbitrarily, with the depth being zero at the coastline. The entire area is divided into three regions. In both the inner and outer regions, existing analytical solutions are used. In the middle region occupying most computational domain, the finite element technique is applied to the governing equation. To obtain the solution, a method of the separation of variables and the Frobenius series are used. The developed solution is validated by comparing it with previously developed analytical solutions.