Numerical solution of water wave propagation problems over variable bathymetries using the modified radial integration boundary element method, Ocean Engineering 257 (2022) 111613

In this paper, a modified radial integration boundary element method (MRIBEM) is applied to the solution of
water wave propagation problem. The mild slope equation which has proved to be a very efficient equation for a
large number of water wave problems is solved using the MRIBEM over arbitrary seabed geometries. The infinite
region is subdivided into a central finite area with irregular seabed and a semi-finite one with parallel depth
contour lines. The interior part is dealt with using MRIBEM and the exterior one is solved using the boundary
element method. This method benefits from the meshfree characteristic of MRIBEM for the inner domain and the
fulfillment of Sommerfeld’s radiation condition for the exterior domain at the same time. Numerical examples
are compared with experimental results and other researches which are indicative of the validity and efficiency
of the present method.