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Computation of incompressible bubble dynamics with a stabilized finite element level set method

机译:用稳定的有限元水平集方法计算不可压缩的气泡动力学

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This paper presents a stabilized finite element method for the three dimensional computation of incompressible bubble dynamics using a level set method. The interface between the two phases is resolved using the level set approach developed by Sethian [Level Set Methods and Fast Marching Methods, Cambridge University Press, 1999], Sussman et al. [J. Comput. Phys. 114 (1994) 146], and Sussman et al. [J. Comput. Phys. 148 (1999) 81-124]. In this approach the interface is represented as a zero level set of a smooth function. The streamline-upwind/Petrov-Galerkin method was used to discretize the governing flow and level set equations. The continuum surface force (CSF) model proposed by Brackbill et al. [J. Comput. Phys. 100 (1992) 335-354] was applied in order to account for surface tension effects. To restrict the interface from moving while re-distancing, an improved re-distancing scheme proposed in the finite difference context [J. Comput. Phys. 148 (1999) 81-124] is adapted for finite element discretization. This enables us to accurately compute the flows with large density and viscosity differences, as well as surface tension. The capability of the resultant algorithm is demonstrated with two and three dimensional numerical examples of a single bubble rising through a quiescent liquid, and two bubble coalescence.
机译:本文提出了一种用水平集方法对不可压缩气泡动力学进行三维计算的稳定有限元方法。这两个阶段之间的接口使用Sethian开发的水平集方法[水平集方法和快速行进方法,剑桥大学出版社,1999],Sussman等人解决。 [J.计算物理114(1994)146]和Sussman等。 [J.计算物理148(1999)81-124]。在这种方法中,接口表示为平滑函数的零级集合。流线上风/ Petrov-Galerkin方法用于离散控制流量和水平集方程。 Brackbill等人提出的连续表面力(CSF)模型。 [J.计算物理为了解决表面张力的影响,应用100(1992)335-354]。为了限制界面在重新平衡时不移动,在有限差分上下文中提出了一种改进的重新平衡方案[J.计算物理148(1999)81-124]适用于有限元离散化。这使我们能够准确计算出具有较大密度和粘度差以及表面张力的流量。通过二维和三维数值示例证明了单个算法通过静态液体上升,两个气泡合并的结果,证明了所得算法的功能。

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