粘弹性流的交错投影格式

IF 1.9 3区 数学 Q2 Mathematics
J. Latché, O. Mokhtari, Yohan Davit, M. Quintard
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引用次数: 1

摘要

我们开发了粘弹性流体流动的数值格式,包括OldroydB和FENE-CR本构模型。空间离散是交错的,对结构化非均匀网格使用标记-单元(MAC)方案,对一般四边形或六面体网格使用Rannacher和Turek (RT)非一致性低阶有限元近似。时间离散采用分步算法,先用投影法求解Navier-Stokes方程,然后用有限体积格式求解构象张量的输运-反应方程。为了获得一致性,采用MAC格式的弱形式推导了动量平衡方程中应力张量弹性部分散度的空间离散化。出于稳定性和准确性的考虑,构象张量的输运-反应方程的求解分为纯对流步骤和反应步骤,前者将变量更改为对数构象张量,后者通过具有局部子循环的欧拉格式求解每个单元一个ODE。对1以上Weissenberg数下的盖驱动腔内流动和受限圆柱体周围流动的数值计算证实了该方案的有效性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A staggered projection scheme for viscoelastic flows                                                              
We develop a numerical scheme for the flow of viscoelastic fluids, including the OldroydB and FENE-CR constitutive models. The space discretization is staggered, using either the Marker-And-Cell (MAC) scheme for structured nonuniform grids, or the Rannacher and Turek (RT) nonconforming low-order finite element approximation for general quandrangular or hexahedral meshes. The time discretization uses a fractional-step algorithm where the solution of the Navier-Stokes equations is first obtained by a projection method and then the transport-reaction equation for the conformation tensor is solved by a finite volume scheme. In order to obtain consistency, the space discretization of the divergence of the elastic part of the stress tensor in the momentum balance equation is derived using a weak form of the MAC scheme. For stability and accuracy purposes, the solution of the transport-reaction equation for the conformation tensor is split into pure convection steps, with a change of variable to the log-conformation tensor, and a reaction step, which consists in solving one ODE per cell via an Euler scheme with local sub-cycling. Numerical computations for the flow in the lid-driven cavity at Weissenberg numbers above one and the flow around a confined cylinder confirm the efficiency of the scheme.
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来源期刊
CiteScore
2.70
自引率
5.30%
发文量
27
审稿时长
6-12 weeks
期刊介绍: M2AN publishes original research papers of high scientific quality in two areas: Mathematical Modelling, and Numerical Analysis. Mathematical Modelling comprises the development and study of a mathematical formulation of a problem. Numerical Analysis comprises the formulation and study of a numerical approximation or solution approach to a mathematically formulated problem. Papers should be of interest to researchers and practitioners that value both rigorous theoretical analysis and solid evidence of computational relevance.
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