论文标题
保守艾伦 - 卡方方程的离散统一气体动力学方案
Discrete unified gas kinetic scheme for the conservative Allen-Cahn equation
论文作者
论文摘要
在本文中，提出了对保守的Allen-CAHN方程（CACE）的离散统一气体动力学方案（DUGK）。在Dugks的背景下，分析了先前Dugks中线性重建的通量评估中恢复的动力学方程。发现跨单元界面的计算微升值仅是针对目标动力学方程的解决方案，这可能会导致cace不准确，因为涉及力项，或者碰撞模型的第一瞬间没有保护特性。为了正确地恢复到二阶准确度的动力学方程，抛物线重建而不是线性重建，将沿着细胞界面处沿特征线传播的分布函数值沿特征线传播的分布函数。为了验证目前的dugks对于CACE的准确性，已经模拟了几个基准问题，包括圆形界面的对角线翻译，Zaleska磁盘的旋转和圆形界面的变形。 数值结果表明，与先前的Dugks相比，当前的Dugks方案能够以提高的精度捕获界面。
In this paper, the discrete unified gas kinetic scheme (DUGKS) with an improved microflux across the cell interface for the conservative Allen-Cahn equation (CACE) is proposed. In the context of DUGKS, the recovered kinetic equation from the flux evaluation with linear reconstruction in the previous DUGKS is analyzed. It is found that the calculated microflux across the cell interface is only the solution to the target kinetic equation with first order accuracy, which can result in an inaccurate CACE since the force term is involved or the first moment of the collision model has no conservation property. To correctly recover the kinetic equation up to the second order accuracy, the value of the distribution function that will propagate along the characteristic line with ending point at the cell interface is appropriated by the parabolic reconstruction instead of the linear reconstruction. To validate the accuracy of the present DUGKS for the CACE, several benchmark problems, including the diagonal translation of a circular interface, the rotation of a Zaleska disk and the deformation of a circular interface, have been simulated. Numerical results show that the present DUGKS scheme is able to capture the interface with improved accuracy when compared with the previous DUGKS.
