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

This paper presents the stationary Bingham fluid flow simulations past a circular cylinder placed in a channel. The governing equations of motion are discretized using the mixed finite element method. The biquadratic element Q2 is used to approximate the velocity space and P1disc for the pressure space. This LBB-stable finite element pair Q2/P1disc\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Q_{2} /P_{1}^{\text{disc}}$$\end{document} leads to an accuracy of third and second order in L2-norm for velocity and pressure approximations, respectively. The discrete version of the nonlinear system is linearized by the Newton’s method, and the linear subproblems as an inner loop are coped with UMFPACK solver. Code validation and grid independence study is also presented to confirm the reliability of the results. Simulations are carried out for various values of dimensionless Bingham number Bn, and its impact is investigated with great detail by demonstrating the velocity, viscosity and pressure contours. The benchmark quantities like drag coefficient (CD) and lift coefficient (CL) are also discussed graphically and quantitatively. Moreover, two different locations of the circular cylinder are considered for the analysis of hydrodynamic forces.