寧建國(guó) 馬天寶 王成

摘 要：爆炸與沖擊問(wèn)題是一個(gè)幾何、材料和邊界條件均為非線性的強(qiáng)耦合問(wèn)題，涉及高速、高壓、高溫，氣體、液體和固體等多種介質(zhì)間的相互作用，針對(duì)該類問(wèn)題進(jìn)行數(shù)值模擬，不僅需要對(duì)多介質(zhì)在強(qiáng)沖擊載荷作用下的瞬態(tài)大變形以及高密度比不同介質(zhì)間運(yùn)動(dòng)界面進(jìn)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(dòng)態(tài)本構(gòu)及破碎、融化和汽化等復(fù)雜非線性力學(xué)行為的建模理論與高精度數(shù)值方法，這些都對(duì)大規(guī)模計(jì)算提出了超常規(guī)要求，也是計(jì)算爆炸力學(xué)中前沿與挑戰(zhàn)性問(wèn)題。該文研究了爆轟波與沖擊波等強(qiáng)間斷問(wèn)題的高精度WENO格式，并針對(duì)爆轟波傳播的高精度計(jì)算中會(huì)出現(xiàn)密度或壓力為負(fù)導(dǎo)致計(jì)算中止的問(wèn)題，構(gòu)造了守恒的三維有限差分WENO保正計(jì)算格式，克服了傳統(tǒng)方法直接將負(fù)值置0或取絕對(duì)值從而破壞守恒性的缺點(diǎn)。此外，針對(duì)三維爆炸與沖擊問(wèn)題大規(guī)模并行計(jì)算的需求，研究了Euler并行算法實(shí)現(xiàn)的關(guān)鍵性問(wèn)題，開(kāi)發(fā)了基于MPI的三維爆炸與沖擊問(wèn)題大規(guī)模并行計(jì)算軟件EXPLOSION-3D，并提出了一套實(shí)用的軟件測(cè)試方案。結(jié)合聚能射流形成過(guò)程的數(shù)值模擬算例，測(cè)試了加速比、并行效率及可擴(kuò)放性，并分析了影響并行性能的因素。最后通過(guò)典型三維爆炸與沖擊問(wèn)題的數(shù)值模擬驗(yàn)證了該軟件解決實(shí)際工程問(wèn)題的能力。該工作的主要?jiǎng)?chuàng)新點(diǎn)是解決了歐拉方法高精度保正性計(jì)算的難題，并提出了一種歐拉數(shù)值方法的并行化策略，從而實(shí)現(xiàn)了爆炸與沖擊問(wèn)題的大規(guī)模計(jì)算，計(jì)算規(guī)?？蛇_(dá)到1億網(wǎng)格以上，有效地解決了商業(yè)軟件無(wú)法計(jì)算的大規(guī)模復(fù)雜爆炸場(chǎng)問(wèn)題。

關(guān)鍵詞：爆炸與沖擊 數(shù)值模擬 高精度格式 并行計(jì)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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