A balanced-force algorithm for continuous and sharp interfacial surface tension models within a volume tracking framework
A balanced-force algorithm for continuous and sharp interfacial surface tension models within a volume tracking framework
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DOI：
10.1016/j.jcp.2005.08.004
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发表时间：
2006-03
期刊：
影响因子：
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通讯作者：
M. Francois;S. J. Cummins;E. Dendy;D. Kothe;J. Sicilian;M. W. Williams
中科院分区：
文献类型：
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作者：
M. Francois;S. J. Cummins;E. Dendy;D. Kothe;J. Sicilian;M. W. Williams
提出了一种新的平衡力算法，用于模拟具有表面张力的界面流动。该算法的特点是用体积分数表示界面的压力校正法。在这个流动算法中，我们设计了一个连续的(例如，连续的表面张力模型)和一个尖锐的(例如，幽灵流体方法)界面表示法来表示由表面张力引起的界面压力跳跃条件。通过从体积分数临时重构距离函数，实现了尖锐的界面表示。我们证明了一种旨在制定力平衡的流动算法在表面张力和由此产生的压力梯度之间保持了精确的平衡。这一平衡既适用于界面表面张力的连续表示，也适用于其尖锐表示。该算法设计消除了更精确的表面张力驱动流动模型的一个难以捉摸的障碍，剩下的就是准确的曲率估计。为了验证我们的公式，我们给出了二维和三维的平衡(静态)液滴的结果，该液滴在界面上具有任意的密度跃迁。我们发现，尖锐的表面张力方法在界面上产生突然的压力跳跃，而连续表面张力方法产生更平滑的转变。然而，这两种方法产生的伪速度都是相同量级的，其根源完全是曲率误差造成的。文中还给出了动态结果，说明了该方法的通用性。
A new balanced-force algorithm is presented for modeling interfacial flow with surface tension. The algorithm is characterized by a pressure-correction method with the interfaces represented by volume fractions. Within this flow algorithm, we devise a continuous (e.g., continuum surface tension model) and a sharp (e.g., a ghost fluid method) interface representation of the surface-tension-induced interfacial pressure jump condition. The sharp interface representation is achieved by temporarily reconstructing distance functions from volume fractions. We demonstrate that a flow algorithm designed to legislate force balance retains an exact balance between surface tension forces and the resulting pressure gradients. This balance holds for both continuous and sharp representations of interfacial surface tension. The algorithm design eliminates one of the elusive impediments to more accurate models of surface tension-driven flow, the remaining of which is accurate curvature estimation. To validate our formulation, we present results for an equilibrium (static) drop in two and three dimensions having an arbitrary density jump across the interface. We find that the sharp surface tension method yields an abrupt pressure jump across the interface, whereas the continuous surface tension method results in a smoother transition. Both methods, however, yield spurious velocities of the same order, the origin of which is due solely to errors in curvature. Dynamic results are also presented to illustrate the versatility of the method.