Modeling of axisymmetric viscous flows of incompressible fluid by the boundary element method

In this paper, the derivation of the fundamental velocity and traction tensor components is presented for Stokes equations in the cylindrical coordinate system for axisymmetric viscous flows. The derivation is based on a three-dimensional singular solution in Cartesian coordinates. Using the presented formulas, the boundary integral equations are constructed in accordance with the potential theory conception. A simple numerical solution algorithm that is an implementation of principles of the indirect boundary element method is proposed. Reliability of the results is verified by solving a test problem the role of which is played by the problem about a flow in a cylindrical tube (the Poiseuille flow) with mixed boundary conditions. The developed method of solving boundary problems for Stokes equations can be used for modeling creeping flows of a viscous fluid with a free surface.