摘要
本文采用对数构象方法,结合同位网格有限体积离散,对由Oldroyd-B本构模型描述的粘弹性流体流动的高We数问题(High Weissenberg Number Problem,HWNP)进行了研究,对等温不可压条件下的平面Poiseuille流和4:1平板收缩流进行了数值模拟.平面Poiseuille流在不同We数时的数值结果验证了对数构象方法在简单流动中的有效性.在4:1粘弹性收缩流的数值模拟中,对数构象方法和传统方法在低We数时流场中的流线、应力等的对比结果验证了对数构象方法在复杂流动中的有效性.高We数时的数值结果表明:对于Oldroyd-B模型,对数构象方法可提高求解时的稳定性,并可将临界We数由传统方法的2.5提高到5.0.
In this paper, a log-conformation tensor finite volume method, which couples the log- conformation tensor approach with the finite volume discretization on non-staggered grids, is proposed to solve the high Weissenberg number problem (HWNP) in viscoelastic flows. The planar Poiseuille flow for Oldroyd-B model is simulated to verify the validity of the method for simple flow. The efficiency and reliability of the log-conformation tensor finite volume method for solving complex flow are shown through the perfect agreement with traditional approach for the simulation of 4:1 planar contraction flow at lower Weissenberg number. The successful simulation at higher critical Weissenberg number 5.0, compared to that of 2.5 in traditional method, indicates that the numerical instability at high Weissenberg number can be overcome by the log-conformation tensor finite volume method.
出处
《工程数学学报》
CSCD
北大核心
2012年第5期703-714,共12页
Chinese Journal of Engineering Mathematics
基金
国家重点基础研究发展计划(2012CB025903)~~
关键词
对数构象
粘弹流体
HWNP
有限体积法
平板收缩流
log-conformation
viscoelastic fluid
HWNP
finite-volume method
planar contraction