Application of the error estimation technique in the method of fundamental solutions for solving incident wave problem with multiple cylinders

This article attempts to solve the problem of oblique incident wave with multiple cylinders using the method of fundamental solutions (MFS) combined with a proposed error estimation technique. In real engineering, many problems only have an empirical result without an exact solution. There are three advantages to the proposed error estimation technique. First, the error estimation technique can provide a reliable solution to approximate the analytical solution. Second, the optimal number of points for the source and collocation points can be determined. Third, a scheme refinement of adaptive distribution of source points can be developed employing the error estimation technique. The theory of single-layer and double-layer potential formulas in the MFS method is considered in this paper. The numerical examples include water wave passing through one, two, and four circular cylinders, respectively. The results show the resultant forces on the cylinder and free surface elevation around the cylinder, respectively. The results are then presented.