Numerical Simulations of the Square Lid Driven Cavity Flow of Bingham Fluids Using Nonconforming Finite Elements Coupled with a Direct Solver

Abstract

In this paper, numerical simulations are performed in a single and double lid driven square cavity to study the flow of a Bingham viscoplastic fluid. The governing equations are discretized with the help of finite element method in space and the nonconforming Stokes elementQ~1/Q0is utilized which gives 2nd-order accuracy for velocity and 1st-order accuracy for pressure. The discretized systems of nonlinear equations are treated by using the Newton method and the inner linear subproablems are solved by the direct solver UMFPACK. A qualitative comparison is done with the results reported in the literature. In addition to these comparisons, some new reference data for the kinetic energy is generated. All these implementations are done in the open source software package FEATFLOW which is a general purpose finite element based solver package for solving partial differential equations.

On Flows of Bingham-Type Fluids with Threshold Slippage

“…Starting with the pioneering works by Mosolov and Miasnikov [6] and Duvaut and Lions [7], a large number of mathematicians have worked on the theoretical analysis of Bingham fluids and other similar viscoplastic media (see [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] and the references therein).…”

Finite element simulations for stationary Bingham fluid flow past a circular cylinder

“…Such approaches with some comparisons are discussed in [13]. Some recent studies on Bingham fluids are reported in [14][15][16]. Over the last two decades or so, flow around obstacles has been emerged as a very important benchmark problem due to its extensive applications in engineering science [17][18][19].…”

Flow of the Bingham-Papanastasiou Regularized Material in a Channel in the Presence of Obstacles: Correlation between Hydrodynamic Forces and Spacing of Obstacles

“…The materials like toothpaste and tomato ketchup are yield stress oriented. The rheology of such is investigated by many researchers [18][19][20][21][22][23][24]. There are some recent discussion and hypothesis about the existence of yield stress.…”