Bingham Flows in Periodic Domains of Infinite Length

作     者：Patrizia DONATO Sorin MARDARE Bogdan VERNESCU Patrizia DONATO;Sorin MARDARE;Bogdan VERNESCU

作者机构：Dedicated to Philippe G. Ciarlet on the occasion of his 80th birthda 

出 版 物：《Chinese Annals of Mathematics,Series B》 (数学年刊（B辑英文版）)

年 卷 期：2018年第39卷第2期

页      面：183-200页

核心收录：

学科分类：080103[工学-流体力学] 08[工学] 0801[工学-力学（可授工学、理学学位）] 

基　　金：supported by the University of Rouen and the Fédération Normandie Mathématiques  respectively 

主　　题：Bingham fluids Variational inequalities 

摘      要：The Bingham fluid model has been successfully used in modeling a large class of non-Newtonian fluids. In this paper, the authors extend to the case of Bingham fluids the results previously obtained by Chipot and Mardare, who studied the asymptotics of the Stokes flow in a cylindrical domain that becomes unbounded in one direction, and prove the convergence of the solution to the Bingham problem in a finite periodic domain, to the solution of the Bingham problem in the infinite periodic domain, as the length of the finite domain goes to infinity. As a consequence of this convergence, the existence of a solution to a Bingham problem in the infinite periodic domain is obtained, and the uniqueness of the velocity field for this problem is also shown. Finally, they show that the error in approximating the velocity field in the infinite domain with the velocity in a periodic domain of length 2l has a polynomial decay in , unlike in the Stokes case （see [Chipot, M. and Mardare, S., Asymptotic behaviour of the Stokes problem in cylinders becoming unbounded in one direction, Journal de Mathgmatiques Pures et Appliqudes, 90（2）, 2008, 133-159]） where it has an exponential decay. This is in itself an important result for the numerical simulations of non-Newtonian flows in long tubes.