Numerical investigation of the boundary layer flow around impulsively moved cylinder

Abstract

In recent years the problem of existing of a smooth solution to the unsteady boundary layer equations with unfavorable (adverse) pressure gradient is frequently discussed in the literature.
The numerical results for schemes with Lagrangian, variables as well as some semi-analytical studies strongly suggest that a singularity evolves after a finite time. The controversy, however, is fueled by the maverick results, obtained by means of Eulerian difference schemes. In the present paper a critical discussion on these approaches is given and for solving the problem a new Eulerian implicit difference scheme of splitting type is developed, which is unconditionally stable in the whole region of flow, including the zone of reversed flow. The results obtained here compare quantitatively very well with the results of Lagrangian numerical schemes and unequivocally indicate that a singularity evolves after a finite time (approximately t 3.0 in dimensionless units).