A new stabilized method for quasi-Newtonian flows

作者：Xie, Chun-mei; Feng, Min-fu^*

来源：Applied Mathematics and Mechanics (English Edition ), 2010, 31(9): 1081-1096.

DOI：10.1007/s10483-010-1344-z

• quasi-Newtonian
• stabilized method
• power law model
• Carreau model
• residual-based posterior bound

For a generalized quasi-Newtonian flow, a new stabilized method focused on the low-order velocity-pressure pairs, (bi)linear/(bi)linear and (bi)linear/constant element, is presented. The pressure projection stabilized method is extended from Stokes problems to quasi-Newtonian flow problems. The theoretical framework developed here yields an estimate bound, which measures error in the approximate velocity in the W (1,r) (Omega) norm and that of the pressure in the L (r')(Omega) (1/r + 1/r' = 1). The power law model and the Carreau model are special ones of the quasi-Newtonian flow problem discussed in this paper. Moreover, a residual-based posterior bound is given. Numerical experiments are presented to confirm the theoretical results.

• 出版日期2010-9
• 单位电子科技大学; 四川大学