一种Lagrange格式及重映算法

从积分形式的二维Lagrange流体力学方程组出发，用有限体积格式进行计算，考虑压力梯度分布对速度和能量改变的影响，构造了在两个控制体上的动量方程的计算格式。在重映算法上，采用积分重映的方法，针对不规则的四边形网格，根据非结构网格的ENO插值的思想，构造线性插值多项式，由于利用其插值点自适应选取的特性，在物理量变化剧烈区域选取最光滑区域的点来插值，虽然不能保持单调性，但只允许出现非常小的振荡。数值结果表明了该方法的可行性。

One Lagrange Scheme and Remapping Algorithm

The finite volume scheme is used for Lagrange equations of hydrodynamics. Because of the influence of pressure gradients upon velocity and energy, a computational scheme is proposed for momentum equation on two control volumes in order to put off the time when the mesh becomes distorted. Besides, according to the ENO interpolation on unstructured grids, a class of linear interpolation polynomial is developed on anomalous quadrilateral grids and allows very small oscillation. Finally, numerical experiments are made with Lagrange method and remapping algorithm. The results show that the method is effective.