Mathematical modeling of one flow in a pipe using the method of $R$-functions

The article deals with the flow in a pipe of rectangular cross section with an inner circular cylindrical element. We use a numerical method that is based on $R$-functions. This method is meshfree and therefore more efficient than the finite element method which requires remeshing when the geometry of the problem is changed. We consider the dependence of the flow on the diameter of the central cylinder and its position in the square pipe under constant pressure gradient. It is found that the resistance decreases when the inner element is displaced from the center of the pipe.