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

• Published in: Advances in Mathematical Physics Vol. 2017; no. 2017; pp. 1 - 10
• Main Authors: Jabeen, K., Yaqub, M., Kousar, N., Mahmood, R.
• Format: Journal Article
• Language: English
• Published: Cairo, Egypt Hindawi Publishing Corporation 01.01.2017; Hindawi; Hindawi Limited; Wiley
• Subjects: Accuracy; Analysis; Computational fluid dynamics; Computer simulation; Energy; Energy (Physics); Finite element analysis; Finite element method; Fluid flow; Mathematical analysis; Mathematical models; Methods; Non-Newtonian fluids; Numerical analysis; Open source software; Reynolds number; Solvers; Viscosity; Yield stress; Islamabad Pakistan
• ISSN: 1687-9120; 1687-9139
• DOI: 10.1155/2017/5210708

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 element Q~1/Q0 is 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.