爆炸與沖擊問題的高精度模擬與大規模數值計算研究

寧建國 馬天寶 王成

摘 要：爆炸與沖擊問題是一個幾何、材料和邊界條件均為非線性的強耦合問題，涉及高速、高壓、高溫，氣體、液體和固體等多種介質間的相互作用，針對該類問題進行數值模擬，不僅需要對多介質在強沖擊載荷作用下的瞬態大變形以及高密度比不同介質間運動界面進行精確的模擬，還涉及到材料在爆炸與沖擊載荷作用下的動態本構及破碎、融化和汽化等復雜非線性力學行為的建模理論與高精度數值方法，這些都對大規模計算提出了超常規要求，也是計算爆炸力學中前沿與挑戰性問題。該文研究了爆轟波與沖擊波等強間斷問題的高精度WENO格式，并針對爆轟波傳播的高精度計算中會出現密度或壓力為負導致計算中止的問題，構造了守恒的三維有限差分WENO保正計算格式，克服了傳統方法直接將負值置0或取絕對值從而破壞守恒性的缺點。此外，針對三維爆炸與沖擊問題大規模并行計算的需求，研究了Euler并行算法實現的關鍵性問題，開發了基于MPI的三維爆炸與沖擊問題大規模并行計算軟件EXPLOSION-3D，并提出了一套實用的軟件測試方案。結合聚能射流形成過程的數值模擬算例，測試了加速比、并行效率及可擴放性，并分析了影響并行性能的因素。最后通過典型三維爆炸與沖擊問題的數值模擬驗證了該軟件解決實際工程問題的能力。該工作的主要創新點是解決了歐拉方法高精度保正性計算的難題，并提出了一種歐拉數值方法的并行化策略，從而實現了爆炸與沖擊問題的大規模計算，計算規模可達到1億網格以上，有效地解決了商業軟件無法計算的大規模復雜爆炸場問題。

關鍵詞：爆炸與沖擊 數值模擬 高精度格式 并行計算

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 its 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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