摘 要：爆炸与冲击问题是一个几何、材料和边界条件均为非线性的强耦合问题，涉及高速、高压、高温，气体、液体和固体等多种介质间的相互作用，针对该类问题进行数值模拟，不仅需要对多介质在强冲击载荷作用下的瞬态大变形以及高密度比不同介质间运动界面进行精确的模拟，还涉及到材料在爆炸与冲击载荷作用下的动态本构及破碎、融化和汽化等复杂非线性力学行为的建模理论与高精度数值方法，这些都对大规模计算提出了超常规要求，也是计算爆炸力学中前沿与挑战性问题。该文研究了爆轰波与冲击波等强间断问题的高精度WENO格式，并针对爆轰波传播的高精度计算中会出现密度或压力为负导致计算中止的问题，构造了守恒的三维有限差分WENO保正计算格式，克服了传统方法直接将负值置0或取绝对值从而破坏守恒性的缺点。此外，针对三维爆炸与冲击问题大规模并行计算的需求，研究了Euler并行算法实现的关键性问题，开发了基于MPI的三维爆炸与冲击问题大规模并行计算软件EXPLOSION-3D，并提出了一套实用的软件测试方案。结合聚能射流形成过程的数值模拟算例，测试了加速比、并行效率及可扩放性，并分析了影响并行性能的因素。最后通过典型三维爆炸与冲击问题的数值模拟验证了该软件解决实际工程问题的能力。该工作的主要创新点是解决了欧拉方法高精度保正性计算的难题，并提出了一种欧拉数值方法的并行化策略，从而实现了爆炸与冲击问题的大规模计算，计算规模可达到1亿网格以上，有效地解决了商业软件无法计算的大规模复杂爆炸场问题。
关键词：爆炸与冲击 数值模拟 高精度格式 并行计算
High Presion and Large Scale Numerical Simulation of Explosion and Shock Problems
Ning Jianguo Ma Tianbao Wang Cheng
（Beijing Institute of Technology）
Abstract：Explosion and shock is a strong coupling problem， and it’s geometric， material and boundary conditions are both nonlinear. The problems often involve high speed， high pressure， high temperature， large deformation and interaction between a variety of material such as gas， liquid and solid. Numerical simulation for this problem not only need to accurately simulate the transient large deformation of various material and interface treatment between multi-material with high ratio of density under strong impact loading， also involves the modeling theory and high precision numerical method of materials with complex nonlinear mechanical behavior like dynamic constitutive and crushing， melting and vaporization under explosion and impact loading. In this paper， the conservation of the three dimensional finite difference WENO computational formats which always ensure its value positive was structured for the suspension of computing problems due to negative density or pressure in the high precision calculation of detonation wave propagation. This algorithm overcome the disadvantages of the traditional method which the negative value 0 or take the absolute value. In addition， the critical problem of the Euler parallel algorithm was studied for the three dimensional explosion and impact problems of large-scale parallel computing. Then the high performance simulation software of three-dimensional explosion and impact problem （EXPLOSION-3D） was designed based on MPI （Message Passing Interface）， and a practical plan of software testing was presented. The speedup， efficiency and scalability of the software were tested based on the numerical example of shaped charge jet， and the effect of the bottlenecks of software was discussed. At last， numerical results of typical three-dimensional explosion and impact problem show the capability of software in dealing with large scale complex engineering problems. The main innovation points of this work are to always ensure the value of high precision format positive， which is the Euler method computing problem. And then we propose parallelization strategies of Euler method， so as to realize the large-scale computing of explosion and impact problem and the computing scale can reach more than 100 million grids. The software can effectively solve the computing of large-scale complex explosion field which the commercial software cannot do.
Key Words：Explosion and shock； Numerical simulation； High precision scheme； Parallel computation
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