用任意拉格朗日——欧拉方法求解流体力学方程组

Arbitrary Lagrangian-Eulerian Computation for Equations of Hydrodynamics

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 ,针对不规则的四边形网格 ,在用次级网格的方法确定网眼内物理量的梯度的基础上 ,提出一种体积加权的方法来构造网眼内的线性插值多项式。将新网格进行了细划 ,先确定新网格小网眼中心点的密度 ,将小网眼的质量直接计算出来 ,再计算新网格的质量 ,然后确定相应的密度 ,从而实现高精度重映。最后用 ALE方法进行数值模拟 。

Finite volume scheme is used for Lagrangian equations of hydrodynamics. Based on the idea of subordinate meshes, a new method of weighted volume used for constructing linear interpolation polynomials is presented. Besides, an conservative remapping algorithm in allusion to the difficulty of integrating the known density distribution in the old mesh over the cell volume. The new mesh is subdivided to calculate the densities of new smaller meshes. Then densities of the new mesh are known and high accuracy remapping is finished. Finally, series of numerical experiments are made with an arbitrary Lagrangian Eulerian (ALE) computing method and results show that the method is effective.