任意拉格朗日—欧拉方法及其在二维数值计算中的初步应用

【作者】 袁帅；

【导师】 李平；

【作者基本信息】 中国工程物理研究院北京研究生部 ， 工程力学， 2003， 硕士

【摘要】 本文简要介绍了ALE方法的研究历史、现状和应用前景，详细阐述了ALE方法的基本理论。并在SALE(Simplified ALE，一种简化的ALE方法，网格可以任意运动，但物质界面处的网格仍然以物质速度运动，物质界面始终为Lagrange网格线以保证网格中只有单物质出现)方法框架下，推导并给出了适用于弹塑性流计算的ALE线积分差分格式。采用Laplace反演方法和速度松弛法计算网格速度，实现了网格的自动重分，采用贡献网格法和线性插值完成输运计算。 借助于ALE方法的早期程序SHALE的基本框架，开发研制了二维弹塑性流ALE方法计算程序HEPALE。程序包含用弹塑性本构模型和Grūnrisen状态方程来描述固体材料的行为；采用JWL状态方程来描述爆轰产物的性质；采用程序燃烧法来模拟爆轰波阵面的传播。 应用HEPALE程序对平面碰撞、铜棒碰撞刚性壁(Taylor杆问题)、爆轰波的传播、炸药驱动金属平板和柱壳进行了数值模拟，并与有关理论解析结果或者实验结果以及LS-DYNA程序、Lagrange程序的计算结果进行了比较，符合程度较好。表明本文的计算方法和程序能够用于爆炸力学诸多有关问题的数值计算。与纯Lagrange程序计算的结果相比较，ALE方法在处理大变形问题时有较明显的优势。更多还原

【Abstract】 The history, development and application of Arbitrary Lagrange-Euler (ALE) are in introduced, and the basic theory of ALE method is also elaborated in detail in this paper. Based on SALE method (Simplified ALE, in which the mesh may move with arbitrarily prescribed velocity with respected to the fluid, and Lagrange interfaces are maintained between cells containing different material.), the line loop integral difference scheme is derived which can be used to calculate two-dimensional elastic-plastic flow. The grid velocity is obtained by using both of so-called Laplace and velocity relaxation methods, and rezone is automatically done. The remap of state variables is calculated with both of donor cell and linear interpolation method.Based on the SHALE code, the early code of ALE, the two dimensional finite difference elastic-plastic flow code HEPALE has been developed, in which the ideal elastic-plastic model and equation of state of Gruneisen are used to describe the solid material, the programmed burn technique is used to simulate the propagation of detonation, and the equation of state of JWL is used to describe the detonation products.With the HEPALE code, the simulated results are reported about problems of plate impact, the copper bar impacted the rigid well (Taylor Bar), the propagation of detonation, and the motion of a plane and a cylinder shell driven by explosives, and they are basically in agreement with experiment, as well as one obtained by LS-DYNA. It is shown that HEPALE code is reasonable and can be applied to simulate dynamic phenomena. It is also shown that the HEPALE code has distinct advantage with the pure Lagrange method in simulating the large distortion problems.更多还原