Explosion mechanics is the theoretical basis for the design of highly efficient arms and ammunition and industrial explosion safety. Because it involves the complex physical and mechanical behaviors of multi-materials under extreme conditions, such as high speed, high temperature and high pressure, it is almost impossible to give exact solutions for explosion problems. As explosion occurs in a very short time and has a strong destructive effect, there will be limited amounts of experimental data obtained during the explosion process. With the continuous development of numerical methods and computer performance, computational explosion mechanics has become a new interdisciplinary branch of explosion mechanics, material dynamics, computational mathematics and computer technology, and greatly promoted the development of explosion mechanics and weapons equipment. Since the late 1960s, US-led western developed countries have developed more than one hundred calculation codes of explosion mechanics. Based on the simulation software for explosion mechanics, calculations about three-dimensional physical processes on a system scale during the course of weapon system development have been performed, which resulted in the development of a number of high efficiency arms and ammunition. Such research institutions as the Beijing Institute of Technology, the Chinese Academy of Engineering Physics, the Institute of Applied Physics and Computational Mathematics, the Institute of Mechanics of the Chinese Academy of Sciences, Peking University, the University of Science and Technology of China and other research institutions have developed different numerical methods for explosion mechanics, dynamic constitutive models and software development. Finite Difference Method and Finite Element Method are the most common methods of the discrete methods adopted in computational explosion mechanics. The former is a representative method by which time and space are covered with cells to gain approximate numerical solutions after partial differential equations (governing equations) are established. The latter is a representative method by which continuous space is decomposed into finite elements. Classed by coordinates, Eulerian method and Lagrangrian Method are two common methods utilized in computational explosion mechanics. On the base of these two methods, two hybrid methods, ALE (Arbitrary Lagrange Euler) and CLE (Coupled Lagrange Euler), are developed. Eulerian method has an advantage in treating the large deformation of materials, which always occurs in explosion mechanics. However, it is difficult to handle mixed cells using this method if the studied system includes multi-materials because a transition region forms along the interface which becomes fuzzy between materials. How to determine the position of interfaces and how to calculate the physical quantities in the mixed cells have been difficult problems in Eulerian codes. PIC (Particle in Cell) method and VOF (Volume of Fluid) method are the traditional methods to solve the interface problems in Eulerian codes. Youngs method can determine the interface clearly by transporting fluid of cells around the interface, becoming the mainstream of VOF methods. The original Youngs method just determines the interface in a mixed cell, and cannot determine the transport order and quantity of material. That is a problem of Eulerian methods. A modified Youngs method is adopted in [1], in which the material’s fractions are adopted to determine the transport order of material. Ref. [2] proposes an interface treatment method, in which the interface curve of material is traced by a series of straight-line segments which connect head and tails, and the material interface is determined by marker line located on the grid lines. Ref. [3] proposed a hybrid VOF and PIC multi-material interface treatment method, in which PIC method is utilized in the important regions, and continuous method is used in the other, resulting in high precision and high efficiency of algorithm by which the deformation of material is tracked successfully during penetration. Another method, Level Set, has been proposed and widely used in recent years. In [4], Level Set method combined with Ghost Fluid method is employed to track the
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