A mixed formulation of the Bingham fluid flow problem: Analysis and numerical solution

作者：Aposporidis Alexis^*; Haber Eldad; Olshanskii Maxim A; Veneziani Alessandro

来源：Computer Methods in Applied Mechanics and Engineering, 2011, 200(29-32): 2434-2446.

DOI：10.1016/j.cma.2011.04.004

• Non-Newtonian flow
• Bingham fluid
• Mixed formulation
• Augmented formulation
• Regularization

In this paper we introduce a mixed formulation of the Bingham fluid flow problem. We consider both the original and a regularized version of the problem, where a parameter E is introduced, forcing the entire domain to be formally a fluid region. In general, common solvers for the regularized problem experience a performance degradation when the parameter E gets smaller. The method studied here introduces an auxiliary tensor variable and shows enhanced numerical properties for small values of E. A good performance is also observed for the non-regularized case. The well posedness for the regularized problem and the equivalence - at the continuous level - between the original (primitive variables) and the mixed formulation are demonstrated. We analyze properties of linearized problems that are relevant for the convergence of numerical solvers. A finite element method for the mixed formulation is discussed. Numerical results confirm the predicted better performances of the mixed formulation when compared to the primitive variables formulation. A comparison to a non-regularized solver based on the augmented Duvaut-Lions-Glowinski formulation of the problem is carried out as well.

• 出版日期2011