欧拉流体力学数值方法中的界面计算

本文所提算法适用于二维和三维多介质流体力学两步欧拉数值方法中输运计算的混合网格(包括自由面网格)界面处理。在一个混合网格中，界面被近似地看作直线(二维)或平面(三维)。整个方法分为三步：(1)第一步，用混合网格周围的八个网格的介质面积份额(二维)或二十六个网格的介质体积份额(三维)确定界面的法线方向；第二步，用混合网格的本身的介质面积份额(二维)或体积份额(三维)确定界面的方程(位置)；第三步，用此直线方程求出通过网格边界的流以及下一时刻网格的面积份额(二维)或体积份额(三维)。最后给出了用此方法所做的一些数值计算及与SLIC算法的比较。

Interface calculations in numerical method for Eulerian hydrodynamics

The algorithm proposed in this paper can be used to deal with interface of mixed cell (including free surface cell) in remapping step of twostep 2-d and 3-d multi-component Eulerian hydrodynamics numerical methods. In a mixed cell the interface is regarded as a straight line in 2-d problems or plane in 3-d problems. The whole method is composed of three steps: (1) Using area fractions of eight cells in 2-d problems or volume fractions of twenty six cells in 3-d problems surrounding the mixed cell to determine the normal orientation of the interface. (2) Determining the equation (position) of the interface with the area fraction (2-d) or volume fraction (3-d) of the mixed cell. (3) Calculating the flux passing across the boundary of cell, and area fraction (2-d) or volume fraction (3-d) of cell at next time. In the last part of this paper, some 2-d and 3-d results of calculation in comparison with results of MEPH (simplified SLIC) are presented.