非牛顿流固耦合问题的半隐式分区ALE有限元-间断有限元耦合算法研究

The development of semi-implicit partitioned ALE finite element/discontinuous Galerkin method for the non-Newtonian fluid structure interaction

针对非牛顿流固耦合问题,提出了任意拉格朗日-欧拉(arbitrary Lagrangian-Eulerian,ALE)框架下的半隐式分区有限元-间断有限元耦合算法。其数学模型主要包括非牛顿流体和固体结构的控制方程,以及流体-固体交界面上的边界条件。固体结构由弹性材料组成,非牛顿流体由幂律型本构模型描述。用分裂格式对非牛顿流体控制方程进行解耦,得到若干子方程;通过有限元、间断有限元方法求解对应恰当类型的子方程。用中心差分及标准有限元方法分别对固体结构弹性动力学方程进行时间和空间离散;用修正的Laplace移动网格方法处理固体结构的形变及流体区域网格的变化过程。最后用数值算法研究了带有圆弧顶端梯形结构体的非牛顿流固耦合问题,并详细分析了结构体高度、入口速度及流体特性等因素对流固耦合问题的影响及机理。

In this paper,we develop the semi-implicit partitioned finite element/discontinuous Galerkin method for the non-Newtonian fluid structure interaction(NFSI) problem within the arbitrary Lagrangian-Eulerian(ALE) framework.The whole mathematical model of this problem involves the governing equations of the non-Newtonian fluid,the solid structure and the boundary conditions on the contacting interface.The structure is composed of elastic solid material and the rheological behavior of non-Newtonian fluid is described according to the power law constitutive equation.The governing system of non-Newtonian fluid is split into several sub-equations and the finite element and discontinuous Galerkin method are employed to solve the appropriate type equations.As for the governing equation of structure,the standard finite element method is chosen to deal with it.In addition,the modified Laplace moving mesh technique is utilized to handle the deformation of the structure and update the interface between the fluid and structure.The problem involving a flexible trapezoidal structure fixed on the bottom of a rectangular tank full of non-Newtonian fluid is investigated.The influences of the height of the structure,the fluid inlet velocity and the behavior of the fluid on the FSI problem are all analyzed.