ﻻ يوجد ملخص باللغة العربية
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.
In this paper, we present an efficient numerical algorithm for solving the time-dependent Cahn--Hilliard--Navier--Stokes equations that model the flow of two phases with different densities. The pressure-correction step in the projection method consi
We extend the positivity-preserving method of Zhang & Shu (2010, JCP, 229, 3091-3120) to simulate the advection of neutral particles in phase space using curvilinear coordinates. The ability to utilize these coordinates is important for non-equilibri
In this paper, we develop an efficient lattice Boltzmann (LB) model for simulating immiscible incompressible $N$-phase flows $(N geq 2)$ based on the Cahn-Hilliard phase field theory. In order to facilitate the design of LB model and reduce the calcu
Phase field methods have been widely used to study phase transitions and polarization switching in ferroelectric thin films. In this paper, we develop an efficient numerical scheme for the variational phase field model based on variational forms of t
In this paper we report on 2D numerical simulations concerning linear and nonlinear evolution of surface-tension-driven instability in two-fluid systems heated from below using classical and phase-field models. In the phase-field formalism, one intro