Arbitrary Lagrangian - Eulerian Approach In The Two-dimensional Numerical Calculation Preliminary Applications

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.