Cessation of annular Poiseuille flows of Bingham plastics

Numerical simulations of cessation flows of a Bingham plastic with the augmented Lagrangian method

“…The problems at hand are made dimensionless using the same scales as those used in Chatzimina et al [1,2]: the lengths are scaled by a characteristic length, L, and the velocity is scaled by a characteristic velocity, U. Then the time is scaled by L 2 / ( being the density and the viscosity), and the pressure and stress are scaled by U/L.…”

“…The objective of the present work is to compare the performance and the results of the former method to the regularized time-dependent 1D results of Chatzimina et al [1,2], in view of the existing theoretical upper bounds of Glowinski [3] and Huilgol et al [4]. The emphasis will be on showing the numerical stopping 0377-0257/$ -see front matter © 2010 Elsevier B.V. All rights reserved.…”

“…Recently, Chatzimina et al [1,2] solved numerically several onedimensional cessation flows of a Bingham plastic, i.e. the plane Couette flow [1], and the plane, round, and annular Poiseuille flows [1,2], in order to compare the numerical stopping times with the theoretical upper bounds obtained by Glowinski [3] and Huilgol et al [4] and study the evolution of the yielded/unyielded regions.…”

“…the plane Couette flow [1], and the plane, round, and annular Poiseuille flows [1,2], in order to compare the numerical stopping times with the theoretical upper bounds obtained by Glowinski [3] and Huilgol et al [4] and study the evolution of the yielded/unyielded regions. The inherent discontinuity of the ideal Bingham plastic model was overcome by using Papanastasiou's exponential regularization [5].…”

“…The numerical results in Refs. [1,2] have been mostly obtained for relatively low values of the regularization parameter, which lead to satisfactory estimates of the stopping times only for moderate and high values of the Bingham number, which is a measure of the fluid yield stress. Chatzimina et al [1,2] pointed out that in order to improve the accuracy of the calculated stopping times at low and moderate Bingham numbers, the regularization parameter should be increased to values that lead to prohibitively very long computation times for such time-dependent calculations.…”