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首页> 外文期刊>Journal of Computational Physics >Physical formulation and numerical algorithm for simulating N immiscible incompressible fluids involving general order parameters
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Physical formulation and numerical algorithm for simulating N immiscible incompressible fluids involving general order parameters

机译：模拟涉及一般阶次参数的N个不混溶不可压缩流体的物理公式和数值算法

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We present a family of physical formulations, and a numerical algorithm, based on a class of general order parameters for simulating the motion of a mixture of N (N >= 2) immiscible incompressible fluids with given densities, dynamic viscosities, and pairwise surface tensions. The N-phase formulations stem from a phase field model we developed in a recent work based on the conservations of mass/momentum, and the second law of thermodynamics. The introduction of general order parameters leads to an extremely strongly-coupled system of (N - 1) phase field equations. On the other hand, the general form enables one to compute the N-phase mixing energy density coefficients in an explicitfashion in terms of the pairwise surface tensions. We show that the increased complexity in the form of the phase field equations associated with general order parameters in actuality does not cause essential computational difficulties. Our numerical algorithm reformulates the (N - 1) strongly-coupled phase field equations for general order parameters into 2(N - 1) Helmholtz-type equations that are completely de-coupled from one another. This leads to a computational complexity comparable to that for the simplified phase field equations associated with certain special choice of the order parameters. We demonstrate the capabilities of the method developed herein using several test problems involving multiple fluid phases and large contrasts in densities and viscosities among the multitude of fluids. In particular, by comparing simulation results with the Langmuir-de Gennes theory of floating liquid lenses we show that the method using general order parameters produces physically accurate results for multiple fluid phases. (C) 2014 Elsevier Inc. All rights reserved.
机译：我们基于一类一般顺序参数，提供了一组物理公式和一个数值算法，用于模拟具有给定密度，动态粘度和成对表面张力的N（N> = 2）不混溶不可压缩流体的混合物的运动。 N相公式源自我们根据质量/动量守恒和热力学第二定律在最近的工作中开发的相场模型。引入一般阶跃参数会导致（N-1）相场方程的极强耦合系统。另一方面，该一般形式使人们能够以成对的表面张力以显式方式计算出N相混合能量密度系数。我们表明，实际上与一般阶次参数关联的相场方程形式的复杂性增加不会引起实质性的计算困难。我们的数值算法将用于一般阶数参数的（N-1）个强耦合相场方程式重构为2（N-1）个Helmholtz型方程式，这些方程式彼此完全解耦。这导致计算复杂性可与与阶数参数的某些特殊选择相关联的简化相场方程相比。我们使用涉及多个流体相的多种测试问题以及众多流体中密度和粘度的大对比来证明本文开发的方法的功能。特别是，通过将仿真结果与浮动液体透镜的Langmuir-de Gennes理论进行比较，我们表明，使用通用阶数参数的方法可为多种流体相产生物理上准确的结果。 （C）2014 Elsevier Inc.保留所有权利。

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