A diffuse domain method for two-phase flows with large density ratio in complex geometries
A diffuse domain method for two-phase flows with large density ratio in complex geometries
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DOI：
10.1017/jfm.2020.790
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发表时间：
2020-11
影响因子：
3.7
通讯作者：
Zhenlin Guo;Fei Yu;P. Lin;S. Wise;J. Lowengrub
中科院分区：
文献类型：
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作者：
Zhenlin Guo;Fei Yu;P. Lin;S. Wise;J. Lowengrub
摘要本文提出了一个准不可压缩Navier-Stokes-Cahn-Hilliard（q-NSCH）扩散界面模型，用于描述具有可变物理性质的两相流体流动，该模型保持了热力学的一致性。然后，我们耦合扩散域方法与这个两相流体模型-产生一个新的q-NSCH-DD模型-模拟两相流动与移动接触线在复杂的几何形状。将原来的复域扩展到一个更大的规则域，通常是一个长方体，复域边界被一个有限厚度的界面区域所代替。引入相场函数来近似原始感兴趣区域的特征函数。原始流体模型q-NSCH在更大的域上重新表述，并添加了近似固体表面边界条件的源项。我们证明了当相场函数引入的扩散畴界面的厚度以$\mathcal {O}（\displaystyle\mathcal {O}）$收缩到零（$\displaystyle\rightarrow 0$）时，q-NSCH-DD系统渐近收敛到q-NSCH系统.我们的分析结果证实了数值测量的误差在$L^{2}$和$L^{\infty }$范数。此外，我们表明，q-NSCH-DD系统不仅允许接触线上移动弯曲的边界，但也使流体-流体界面相交的固体物体在一个角度是一致的，与规定的接触角。
Abstract We present a quasi-incompressible Navier–Stokes–Cahn–Hilliard (q-NSCH) diffuse interface model for two-phase fluid flows with variable physical properties that maintains thermodynamic consistency. Then, we couple the diffuse domain method with this two-phase fluid model – yielding a new q-NSCH-DD model – to simulate the two-phase flows with moving contact lines in complex geometries. The original complex domain is extended to a larger regular domain, usually a cuboid, and the complex domain boundary is replaced by an interfacial region with finite thickness. A phase-field function is introduced to approximate the characteristic function of the original domain of interest. The original fluid model, q-NSCH, is reformulated on the larger domain with additional source terms that approximate the boundary conditions on the solid surface. We show that the q-NSCH-DD system converges to the q-NSCH system asymptotically as the thickness of the diffuse domain interface introduced by the phase-field function shrinks to zero ($\epsilon \rightarrow 0$) with $\mathcal {O}(\epsilon )$. Our analytic results are confirmed numerically by measuring the errors in both $L^{2}$ and $L^{\infty }$ norms. In addition, we show that the q-NSCH-DD system not only allows the contact line to move on curved boundaries, but also makes the fluid–fluid interface intersect the solid object at an angle that is consistent with the prescribed contact angle.