A level set method for materials with texturally equilibrated pores
A level set method for materials with texturally equilibrated pores
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DOI：
10.1016/j.jcp.2015.05.023
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发表时间：
2015-09-15
影响因子：
4.1
通讯作者：
Prodanovic, Masa
中科院分区：
文献类型：
--
作者：
Ghanbarzadeh, Soheil;Hesse, Marc A.;Prodanovic, Masa
结构平衡控制着许多天然多孔材料中液相的分布，如部分熔融的岩石和合金，盐水和冰水系统。在这些材料中，孔隙几何形状演变为使固-液界面能最小化，同时保持恒定的二面角，在固液接触线上。我们提出了一个水平集方法来计算一个隐式表示的液-固界面的纹理平衡与空间填充镶嵌的多个固体颗粒在三维空间。每个晶粒由一个单独的水平集函数表示，通过将表面扩散下的固液界面演化为常平均曲率表面来实现界面能最小化。液体体积和二面角的限制被添加到制定使用虚拟对流和正常的速度项。这将导致在一个初始值问题的非线性耦合偏微分方程的系统管理的水平集为每个晶粒的演变，使用的固体颗粒作为初始条件的隐式表示。设计了一种区域分解方案，将每个颗粒的计算区域限制在颗粒周围的几个网格点上。在原计算域的更高层次上实现了接口间的耦合。通过高阶空间微分方案和通过域组合的计算局部化，提高了离散化的空间分辨率。三维解决方案的例子也得到了不同的晶粒分布网络，说明几何的灵活性的方法。(C)2015 Elsevier Inc. All rights reserved.
Textural equilibrium controls the distribution of the liquid phase in many naturally occurring porous materials such as partially molten rocks and alloys, salt-brine and ice-water systems. In these materials, pore geometry evolves to minimize the solid-liquid interfacial energy while maintaining a constant dihedral angle,., at solid-liquid contact lines. We present a level set method to compute an implicit representation of the liquid-solid interface in textural equilibrium with space-filling tessellations of multiple solid grains in three dimensions. Each grain is represented by a separate level set function and interfacial energy minimization is achieved by evolving the solid-liquid interface under surface diffusion to constant mean curvature surface. The liquid volume and dihedral angle constraints are added to the formulation using virtual convective and normal velocity terms. This results in an initial value problem for a system of non-linear coupled PDEs governing the evolution of the level sets for each grain, using the implicit representation of the solid grains as initial condition. A domain decomposition scheme is devised to restrict the computational domain of each grain to few grid points around the grain. The coupling between the interfaces is achieved in a higher level on the original computational domain. The spatial resolution of the discretization is improved through high-order spatial differentiation schemes and localization of computations through domain composition. Examples of three-dimensional solutions are also obtained for different grain distributions networks that illustrate the geometric flexibility of the method. (C) 2015 Elsevier Inc. All rights reserved.