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不同密度与粘性的多相流移动接触线问题的自适应有限元方法

施意   

  1. 北京应用物理与计算数学研究所计算物理重点实验室, 北京 100094
  • 收稿日期:2015-08-31 出版日期:2015-12-15 发布日期:2015-12-18
  • 基金资助:

    国家自然科学基金资助项目(1141033, 1141034, 11471049, 11475033);国家高技术研究发展计划(2012AA01A303);中国工程物理研究院院长基金资助项目(201402037);中国工程物理研究院科学技术发展基金资助项目(2015B0202033,2015B0202035);计算物理重点实验室基金资助项目(9140C690104150C69303).

施意. 不同密度与粘性的多相流移动接触线问题的自适应有限元方法[J]. 数值计算与计算机应用, 2015, 36(4): 297-309.

Shi Yi. AN ADAPTIVE FINITE ELEMENT METHOD FOR MOVING CONTACT LINE PROBLEMS WITH DIFFERENT DENSITIES AND VISCOSITIES[J]. Journal of Numerical Methods and Computer Applications, 2015, 36(4): 297-309.

AN ADAPTIVE FINITE ELEMENT METHOD FOR MOVING CONTACT LINE PROBLEMS WITH DIFFERENT DENSITIES AND VISCOSITIES

Shi Yi   

  1. Institute of Applied Physics and Computational Mathematics, Beijing, China
  • Received:2015-08-31 Online:2015-12-15 Published:2015-12-18
本文中,对于具有不同密度与粘性差的多相流移动接触线问题,我们提出了一种自适应有限元方法.我们所使用的模型为Cahn-Hilliard-Navier-Stokes模型,以及其广义Navier边界条件.在时间上,我们使用分裂方法来求解此系统:对于Cahn-Hilliard方程,使用一种基于凸分解的半隐式方法求解;对于Navier-Stokes方程,采用了压力稳定化方法求解.这种方法在满足某些条件下,是能量稳定的,而且对于处理大密度差问题特别有效.在空间上,我们采用了满足LBB条件的有限元方法进行离散,而且基于后验误差估计理论,我们给出了其网格的自适应加密/放粗方法.数值试验证明了我们算法的正确性与有效性.
In this paper, we propose an adaptive finite element method for the moving contact line problems of multi-phase flows with different densities and viscosities. The Cahn-Hilliard-Navier-Stokes system with the generalized Navier boundary condition is employed for our simulation. Splitting method is employed for the system in time:for the Cahn-Hilliard equation, we use the convex-splitting method, and for the Navier-Stokes equation, we use the pressure stabilization method. The method is efficient for problems with large density ratios, and is energy stable under certain conditions. We use the LBB stable finite element method in space. Moreover, we propose the adaptive mesh refinement method based on the a posteriori error estimates for the system. Numerical simulations demonstrates the accuracy and efficiency of our method.

MR(2010)主题分类: 

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