Method of calculating steady-state flows of a viscous fluid with free boundary in vortex-stream function variables

Computations of the motion of a viscous incompressible fluid with a free boundary in vortex-stream function variables entail difficulties in the implementation of boundary conditions on the free surface. A new approach to the formulation of boundary conditions, which takes into account the specifics in giving these conditions on the free boundary is proposed. An efficient numerical method of calculating steady-state flows of a fluid is developed and implemented. Model computations for problems that have exact solutions are performed.