ИСТИНА

The numerical modeling of the unsteady Poiseu ille flows of a viscoplastic medium in channels of different cross-sections is presen ted. Based on augmented Lagrangian method and finite-difference scheme (suggested by the authors) problems of flow cessation are considered. We have examined dependance of time stopping on internal parameters (density, viscosity yield stress and geometry characters of the cross-section). The results obtained are consistent with previously known theoretical upper bounds for time stopping. Our numerical simulation shows peculiarity of the rigid zones distribution which is specific for the unsteady flows. More precisely, dead zones appearing shortly before cessation in triangular, circular and square cross-sections are abutted upon th e whole boundary, and are exceeded critical curves (which bound dead zones in the steady case) for other cross-sections. We demonstrate steady and unsteady flows in the several comp lex domains, namely: L-shaped, semicircular, elliptical, and also domain with re-entrant corners and in the form of a sand glass.