The method of fundamental solutions without fictitious boundary for solving Stokes problems

In this communication we present a simple modification of the method of fundamental solutions applied to Stokes problems, which allows to make coincident the source and collocation points. It is based on a special treatment of the singular kernel evaluations, where spatially averaged quantities are considered by using auxiliary (or fictitious) Stokeslets. The method is still truly meshless and easy to implement.

► Thanks to the modification, we make coincident the source and collocation points.
► We avoid the introduction of a fictitious boundary where source points are located.
► The introduction of a heuristic off-set between boundaries is avoided.
► We have applied the proposed modification to several 2D and 3D Stokes flows.
► Thanks to the modification, the condition number of the kernel matrix is moderate.