Efficient Solutions of Mixed-Type Axial Symmetry Problems for Perfect Fluids

Potential flows of fluids (a perfect fluid in space, a film of viscous incompressible fluid between slabs) are described through harmononic functions. The availability of their countable bases allows for solving not just basic problems (which conventionally involve special functions), but also mixed-type problems with arbitrary types of boundary states. These are efficiently addressed by the numerical analytic method of boundary states. Symmetry cases make it possible to significantly reduce the number of active elements of the basis set and in so doing to save computational power. The study provides a solution of a problem for a perfect fluid flowing in an axially symmetrical pipe, with mixed boundary states.