This technique relies on a uniqueness theorem to generate solutions to boundary value problems involving Poisson's equation in situations with nice geometric arrangements.  
This technique can be used to determine the motion of a line vortex inside a fluid-filled cylinder, or the flow pattern induced by a line vortex near a rigid barrier.  For a point near a circular boundary, the distance of the appropriate point from the circle's center is given by the circle's radius squared over the source or sink distance from the circle's center.  This technique relies on a uniqueness theorem to generate solutions to boundary value problems involving Poisson's equation in situations with nice geometric arrangements.  Commonly used in electrostatics to determine the potential due to a charge near a conducting surface, FTP, name this technique which involves placing a reflected charge in a situation with a mirror symmetry.
This technique can be used to determine the motion of a line vortex inside a fluid-filled cylinder, or the flow pattern induced by a line vortex near a rigid barrier.  
the technique or method of images