Finite element and stream-tube formulations for flow computations—two-dimensional applications

This paper presents a velocity/pressure/function-of-transformation formulation to simulate two- and three-dimensional flows by a finite element Galerkin technique associated to stream-tube analysis. The latter method involves an unknown transformation. Applications are given for plane and axisymmetric flows with slip or no-slip conditions at the wall and with free surfaces. In the mapped domain, two-dimensional streamline Hermite elements, well-adapted to various boundary conditions, are considered. The numerical results for a Newtonian fluid are found to be consistent with those of the literature and highlight singularity effects that arise at the transition zone of change of boundary conditions, in stick-slip and swell flow problems.