Finite element analysis of the duct flow of Bingham plastic fluids: an application of the variational inequality

Application of the augmented Lagrangian method to steady pipe flows of Bingham, Casson and Herschel–Bulkley fluids

“…The Bingham model is the simplest and most widely used model for viscoplastic materials [3,4,[6][7][8][9][10][11][12][15][16][17]19,[25][26][27][28]31]. It has two parameters in the original form.…”

“…Such a method is based on the concept of variational inequalities and its application to Bingham fluids was pioneered by Duvaut and Lions [23]. Since that time, a series of researches have been performed on pipe flows of Bingham fluids [24][25][26][27][28] and general viscoplastic fluids [20,29], flows past a single sphere [23] and two collinearly translating spheres [30], flow past a cylinder [31], multi-layer lubrication flow and counter-current exchange flow [22], cavity driven flow [32] and other problems [33][34][35]. Now, in pipe flows, the existence and uniqueness of a solution to the variational inequality when the problem is posed in a Hilbert space is well known [23], and is applicable to Bingham fluids.…”

On the usage of viscosity regularisation methods for visco-plastic fluid flow computation

“…A partial list (with apologies) is [9,[11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][32][33][34][35][36]. As well as the smooth regularisations (8)- (10), a number of the above studies have used regularisations based on the bi-viscosity model.…”

Numerical solution of duct flows of multiple visco-plastic fluids

“…These two regularised models have been implemented by a range of authors and for many different problems. A partial list of applications of viscosity regularisation is [9,13,[23][24][25][26][27][28][29][30]. There are certainly advantages of the viscosity regularisation methods.…”