Subhedar A, Reiter A, Selzer M, Varnik F, Nestler B
Institute for Digital Materials Science, Karlsruhe University of Applied Sciences, Moltkestraße 30, 76133 Karlsruhe, Germany.
Institute of Applied Materials-Computational Materials Science, Karlsruhe Institute of Technology, Straße am Forum 7, 76131 Karlsruhe, Germany.
Phys Rev E. 2020 Jan;101(1-1):013313. doi: 10.1103/PhysRevE.101.013313.
We study the interface tracking characteristics of a color-gradient-based lattice Boltzmann model for immiscible flows. Investigation of the local density change in one of the fluid phases, via a Taylor series expansion of the recursive lattice Boltzmann equation, leads to the evolution equation of the order parameter that differentiates the fluids. It turns out that this interface evolution follows a conservative Allen-Cahn equation with a mobility which is independent of the fluid viscosities and surface tension. The mobility of the interface, which solely depends upon lattice speed of sound, can have a crucial effect on the physical dynamics of the interface. Further, we find that, when the equivalent lattice weights inside the segregation operator are modified, the resulting differential operators have a discretization error that is anisotropic to the leading order. As a consequence, the discretization errors in the segregation operator, which ensures a finite interface width, can act as a source of the spurious currents. These findings are supported with the help of numerical simulations.
我们研究了用于不混溶流的基于颜色梯度的格子玻尔兹曼模型的界面跟踪特性。通过递归格子玻尔兹曼方程的泰勒级数展开，对其中一个流体相的局部密度变化进行研究，得到了区分流体的序参数的演化方程。结果表明，这种界面演化遵循一个保守的艾伦 - 卡恩方程，其迁移率与流体粘度和表面张力无关。仅取决于格子声速的界面迁移率，可能对界面的物理动力学产生关键影响。此外，我们发现，当修改分离算子内的等效格子权重时，所得微分算子具有到主导阶的各向异性离散误差。因此，确保有限界面宽度的分离算子中的离散误差，可能成为虚假电流的来源。这些发现得到了数值模拟的支持。
