Numerical solution of water wave propagation problems over variable bathymetries using the modified radial integration boundary element method

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.

Automated summary

In this paper, a modified radial integration boundary element method (MRIBEM) is used to solve the water wave propagation problem. The MRIBEM method is applied to solve the mild slope equation over arbitrary seabed geometries, dividing the infinite region into a central finite area and a semi-finite area. The interior part is solved using MRIBEM, while the exterior part is solved using the boundary element method. Numerical examples demonstrate the validity and efficiency of the proposed method, which combines the meshfree characteristic of MRIBEM and the fulfillment of Sommerfeld's radiation condition.