论文标题
二阶保守相位方程的一些理论结果
Some theoretical results on the second-order conservative phase field equation
论文作者
论文摘要
在本文中，提出了关于二阶保守相位场（SOCPF）方程的理论研究。理论结果包括以下三个方面。首先，给出了SOCPF方程的三种新推导方法。 SOCPF方程可被视为梯度流，特殊扩散方程和分段常数函数的尖锐界面公式的扩散界面形式。这些推导方法有助于我们从不同的角度理解SOCPF方程。其次，研究了SOCPF方程溶液的保护特性。与Cahn-Hilliard方程和Allen-Cahn方程相比，SOCPF方程的解决方案满足了更多的保护定律。第三，研究了SOCPF方程的润湿边界条件。我们发现，非畅通边界条件等效于两个组分相位场模型的润湿边界条件。此外，应用$ n $ - 组件相位字段模型的无升华边界条件，我们为$ n $相位字段参数提供了一组润湿边界条件。
In this paper, a theoretical research on the second-order conservative phase field (SOCPF) equation is presented. The theoretical results include the following three aspects. First, three new derivation methods for the SOCPF equation are given. The SOCPF equation can be viewed as the gradient flow, the special diffusion equation and the diffuse interface form of a sharp interface formulation for the piecewise constant function, respectively. These derivation methods help us to understand the SOCPF equation at different perspectives. Second, the conservation's properties of the solution of SOCPF equation are studied. Compared with the Cahn-Hilliard equation and the Allen-Cahn equation, it is found that the solution of SOCPF equation satisfies more conservation laws. Third, the wetting boundary condition for the SOCPF equation is investigated. We find that the no-flux boundary condition is equivalent to the wetting boundary condition for two-component phase field model. Moreover, applying the no-flux boundary conditions for $N$-component phase field model, we give a set of wetting boundary conditions for $N$ phase field parameters.
