Weakly-imposed Dirichlet boundary conditions for non-Newtonian fluid flow

作者：Baltussen M G H M; Choi Y J; Hulsen M A^*; Anderson P D

来源：Journal of Non-Newtonian Fluid Mechanics, 2011, 166(17-18): 993-1003.

DOI：10.1016/j.jnnfm.2011.05.008

• Weakly-imposed Dirichlet boundary conditions
• XFEM
• Generalized Newtonian fluid
• Viscoelastic fluid

We propose a new formulation for weakly imposing Dirichlet boundary conditions in non-Newtonian fluid flow. It is based on the Gerstenberger-Wall formulation for Newtonian fluids [1], but extended to non-Newtonian fluids. It uses a stabilization term in the weak form that is independent from the actual fluid model used, except for an adjustable parameter kappa, having the physical dimension of a viscosity. The new formulation is tested, combined with an extended finite element method, for the flow past a cylinder between two walls using both a generalized Newtonian and a viscoelastic fluid. It is shown that the convergence is optimal for the generalized Newtonian fluid by comparing with a converged boundary-fitted solution using traditional strong boundary conditions. Also the solution of the viscoelastic fluid compares very well with a traditional solution using a boundary-fitted mesh and strong Dirichlet boundary conditions. For both fluid models we also test various values of the kappa parameter and it turns out that a value equal to the zero-shear-viscosity gives good results. But, it is also shown that a wide range of kappa values can be chosen without sacrificing accuracy.

• 出版日期2011-9-18