三维非牛顿流体充填过程的有限元-间断有限元数值模拟研究  

The numerical investigation of non-Newtonian fluid filling process via finite element and discontinuous Galerkin method

作　　者：高普阳 GAO Puyang(School of Science,Chang′an University,Xi′an 710064,China)

机构地区：[1]长安大学理学院,陕西西安710064

出　　处：《浙江大学学报（理学版）》2023年第1期49-55,共7页Journal of Zhejiang University（Science Edition）

基　　金：国家自然科学基金资助项目(11901051,11971075);陕西省自然科学基础研究计划青年项目(2020JQ-338);长安大学中央高校基本科研业务费项目(300102122107);陕西省科学技术协会青年人才托举计划项目(20220504)。

摘　　要：针对三维非牛顿流体充填问题,建立了有限元-间断有限元耦合算法。对于两相Navier-Stokes方程,基于压力增量修正格式分三步求解,分别采用二次和一次拉格朗日插值多项式求解速度和压力,以确保计算过程稳定。采用守恒型水平集(level set)方法追踪运动界面,并依据间断有限元方法求解水平集和重新初始化方程。以三维圆球剪切流动及非牛顿流体三维平板型腔充填过程为例,并与已有文献的数值和实验结果进行比较,以验证数值算法的稳定性、准确性以及流体的质量守恒性。In this paper, we develop a coupled finite element and discontinuous Galerkin method in three dimension and study the non-Newtonian fluid filling process. To solve two phase Navier-Stokes equations, we employ the incremental pressure correction scheme to accomplish it in three steps. In order to guarantee the computational stability, we take the second order and first order interpolation polynomials for the velocity and pressure, respectively. In addition, the conservative Level Set method is employed to capture the moving interface. The discontinuous Galerkin method is used to solve the Level Set and its re-initialization equations. We take the three dimensional vortex shearing problem and the three dimensional non-Newtonian fluid filling process to verify the proposed approach, compare the result with the numerical results and existing experimental data to illustrate the stability, accuracy and the mass conservation property of the coupled scheme.

关 键 词：有限元 间断有限元 水平集 非牛顿充填过程 

分 类 号：O242.1[理学—计算数学]