论文标题
两相流中表面张力效应的变分界面构成和保守的相位方法
A variational interface-preserving and conservative phase-field method for the surface tension effect in two-phase flows
论文作者
论文摘要
我们提出了一种基于有限元的变异界面保护和保守的相位场公式，用于使用表面张力动力学对不可压缩的两相流进行建模。对流Allen-Cahn相位场配方的双曲线切线界面曲线的保存取决于新型的时间依赖性迁移率模型。根据速度的梯度和漫射界面区域中的顺序参数的函数，对迁移系数进行了调节，以使自由能最小化适当地反对对流失真。对流失真与自由能最小化的比率称为对流失真参数，这是由于对流效应而与双曲线切线的偏差。质量保护是通过实施具有时间和空间依赖相位函数的Lagrange乘数来实现的。我们将界面保护和保守的相位场公式与不可压缩的Navier-Stokes方程和连续表面张力力模型进行了模拟，以模拟不可压缩的两相流。使用非结构化有限元元素，使用专为解决方案的界限和稳定性而设计的积极保存方案。我们通过伸展流中的通用一维分散反应系统来检查Allen-CAHN相位求解器的收敛性和准确性。我们相对于对流失真参数量化并系统地评估相对界面厚度误差和相对表面张力力误差。进一步模拟了二维和三维升高的气泡病例，以检查所提出的模型对体积保留平均曲率流和界面保存能力的有效性。
We present a finite element based variational interface-preserving and conservative phase-field formulation for the modeling of incompressible two-phase flows with surface tension dynamics. The preservation of the hyperbolic tangent interface profile of the convective Allen-Cahn phase-field formulation relies on a novel time-dependent mobility model. The mobility coefficient is adjusted adaptively as a function of gradients of the velocity and the order parameter in the diffuse interface region in such a way that the free energy minimization properly opposes the convective distortion. The ratio of the convective distortion to the free energy minimization is termed as the convective distortion parameter, which characterizes the deviation from the hyperbolic tangent shape due to the convection effect. The mass conservation is achieved by enforcing a Lagrange multiplier with both temporal and spatial dependence on the phase-field function. We integrate the interface-preserving and conservative phase-field formulation with the incompressible Navier-Stokes equations and the continuum surface tension force model for the simulation of incompressible two-phase flows. A positivity preserving scheme designed for the boundedness and stability of the solution is employed for the variational discretization using unstructured finite elements. We examine the convergence and accuracy of the Allen-Cahn phase-field solver through a generic one-dimensional bistable diffusion-reaction system in a stretching flow. We quantify and systematically assess the relative interface thickness error and the relative surface tension force error with respect to the convective distortion parameter. Two- and three-dimensional rising bubble cases are further simulated to examine the effectiveness of the proposed model on the volume-preserving mean curvature flow and the interface-preserving capability.
