一种改进的高效并行爆轰冲击波动力学算法及验证与确认

doi:10.12382/bgxb.2025.0411

摘要/Abstract

摘要：

在均匀二维/三维笛卡尔网格上,数值离散和求解基于爆轰冲击波动力学(Detonation Shock Dynamics, DSD)理论的level set方程,得到的炸药稳定传播爆轰波阵面到达时刻,可用于流体动力学数值模拟的程序燃烧算法。简化和改进了DSD边界条件算法,包括边界节点模板选取方法,及边界节点排序方法。研制了消息传递接口与共享存储多线程混合并行程序DSDLS,可高效求解大规模爆轰问题。利用一系列解析解、半解析解,以及爆轰实验,对算法及程序进行了验证与确认。数值模拟得到的爆轰波走时结果与精确解、实验数据相符。超10亿节点网格大规模并行测试表明,DSDLS程序具有良好的并行效率及可扩展性。

关键词: 爆轰冲击波动力学, 均匀笛卡尔网格, 混合并行, 数值模拟

Abstract:

The equation of level set function based on DSD (Detonation Shock Dynamics) theory is numerically discretized and solved on uniform 2D/3D Cartesian grid. The obtained TOA (Time of Arrival) for the stable detonation front in the high explosive can be used by program burn algorithm in the hydrodynamic simulations. The boundary condition algorithm, including the selection method of boundary node stencils, and the method of boundary node sort, is simplified and improved based on the previous works. The hybrid MPI (Message-Passing Interface) and OpenMP (Open Multi-Processing) parallel code DSDLS is developed for the efficient solutions of large-scale explosive detonation problems. A series of analytic solutions, semi-analytic solutions, and explosive detonation experiments are used for verification and validation of the proposed improved DSD algorithm, which indicate that the detonation front TOA of numerical simulations conform to the exact solutions and the measured data of experiments. The results of large-scale parallel test on the grid of over 10⁹ nodes indicate that DSDLS is of good parallel efficiency and parallel scalability.

Key words: DSD, uniform Cartesian grid, hybrid parallel method, numerical simulation

熊俊, 代仪军, 宫翔飞, 刘鲁峰. 一种改进的高效并行爆轰冲击波动力学算法及验证与确认[J]. 兵工学报, 2025, 46(10): 250411-.

XIONG Jun, DAI Yijun, GONG Xiangfei, LIU Lufeng. An Improved Efficient Parallel DSD Algorithm and Its Verification & Validation[J]. Acta Armamentarii, 2025, 46(10): 250411-.

图/表 25

图1 炸药区域边界与爆轰波阵面level set函数示意图

Fig.1 Convention used to define the level set regions for the high explosive region boundary and the detonation front

图2 炸药边界上爆轰波阵面与惰性材料相互作用的边界角示意图

Fig.2 The interaction of a detonation front with the boundary of an inert material

图3 边界节点多个候选模板示例

Fig.3 Example of boundary node with multiple stencil candidates

图4 二维情况下边界节点的2种候选模板类型

Fig.4 The two orthogonal stencils of local 2D boundary condition algorithm

图5 二维区域分解示意图

Fig.5 Schematic diagram of 2D domain decomposition

图6 DO循环语句块OpenMP并行Fortran代码片段

Fig.6 Code snippet of OpenMP parallelism for Fortran statement block of DO cycle

图7 三维情况下边界节点的3种候选模板类型

Fig.7 The three orthogonal stencils of local 3D boundary condition algorithm

图8 外爆球形爆轰波问题的爆轰波阵面到达时刻等值线

Fig.8 Contours of detonation front TOA for the expanding sphere detonation problem

表1 外爆球形爆轰波问题的网格收敛率

Table 1 Grid convergence rate for the expanding sphere detonation problem

单元尺寸h	误差E₁	收敛阶
1/40	5.5335×10^-4	-
1/80	1.0581×10^-4	2.38
1/160	2.8199×10^-5	1.90
1/320	6.9404×10^-6	2.02

图9 炸药柱爆轰波问题构型示意图

Fig.9 Configuration of the rate stick detonation problem

图10 炸药柱爆轰波问题的爆轰波阵面到达时刻等值线

Fig.10 Contours of detonation front TOA for the rate stick detonation problem

表2 炸药柱爆轰波问题的参考解

Table 2 The reference solutions for the rate stick detonation problem

点编号	x	y^e=f(x,t)
1	0.00	5.902965
2	0.52	5.858715
3	0.96	5.696289

图11 炸药柱爆轰波问题:x=0处纵坐标计算误差收敛情况对比

Fig.11 Resolution study for the rate stick detonation problem: error in y location with respect to the reference lution at x=0 and burntime=5.0

图12 炸药环爆轰波问题构型示意图

Fig.12 Configuration of the explosive arc detonation problem

图13 炸药环爆轰波问题的爆轰波阵面到达时刻等值线

Fig.13 Contours of detonation front TOA for the explosive arc detonation problem

图14 典型位置处爆轰波到达时刻计算误差随网格单元尺寸的变化

Fig.14 Error in burn arrival times with respect to the “exact” solutions, recorded at (3.5, 0.0) and (1.5, 2.0) with varying DSD grid spacing

图15 Passover绕爆实验装置示意图

Fig.15 Assembly sketch for DSD Passover validation experiment

表3 Passover实验PBX 9501炸药和铅的材料参数

Table 3 The material parameters of PBX 9501 and lead for the DSD simulation of passover experiment

材料	参数	数值
PBX 9501	D_CJ/(km·s^-1)	8.86
	α₀/cm	0.04
PBX 9501/铅	ω_c	66°
	ω_s	35°

图16 计算结果

Fig.16 Results of simulation

图17 Passover实验、DSD计算得到的爆轰波到达炸药柱上表面的时间与实验数据及文献提供的DSD、DNS计算结果的对比

Fig.17 Time of arrival at the top surface of the device for the passover experiment, comparison of experiments, DNS and DSD simulations

图18 Cyclops实验装置横截面构型示意图

Fig.18 Cross-section schematic of the Cyclops experiment

表4 Cyclops实验DSD模型相关材料参数

Table 4 The material parameters for the DSD simulation of Cyclops experiment

材料	参数	数值
PBX 9501	D_CJ/(km·s^-1)	8.81
	α₀/cm	0.04
PBX 9502	D_CJ/(km·s^-1)	7.80
	α₀/cm	0.08
PBX 9502/钢	ω_c	65°
	ω_s	58°
PBX 9502/锡	ω_c	62°
	ω_s	58°

图19 Cyclops实验,DSD计算得到的爆轰波阵面到达时刻等值线及与实验数据的对比

Fig.19 Contours of detonation front TOA for the Cyclops experiment compared to the detonation isochrone position data

表5 MPI并行效率测试

Table 5 Test of MPI parallel efficiency

进程数	墙钟时间/s	并行效率/%
16	55092	-
32	29556	93.2
64	15362	89.7
128	7942	86.7
256	4216	81.7
512	2205	78.1
1024	1172	73.4
2048	668	64.4
4096	386	55.8
8192	248	43.4

表6 MPI+OpenMP混合并行效率测试

Table 6 Efficiency test of hybrid MPI and OpenMP parallel programming

算例编号	进程数	线程数	墙钟时间/s
1	32	1^*	805
2	32	1	825
3	32	2	560
4	64	1	482
5	64	2	354

参考文献 30

[1]	ASLAM T D. Shock temperature dependent rate law for plastic bonded explosives[J]. Journal of Applied Physics, 2018, 123(14): 145901.
[2]	CRAVEN G T, PRICE M A, ANDREWS S A, et al. AWSD reactive flow model for PBX 9404[J]. Journal of Applied Physics, 2025, 137(13): 135903.
[3]	BDZIL J B, STEWART D S, JACKSON T L. Program burn algorithms based on detonation shock dynamics: discrete approximations of detonation flows with discontinuous front models[J]. Journal of Computational Physics, 2001, 174(2): 870-902.
[4]	BDZIL J B, STEWART D S. Theory of detonation shock dynamics[M]// Berlin: Springer, 2012.
[5]	ASLAM T D, BDZIL J B, STEWART D S. Level set methods applied to modeling detonation shock dynamics[J]. Journal of Computational Physics, 1996, 126(2): 390-409.
[6]	HERNÁNDEZ A, BDZIL J B, STEWART D S. An MPI parallel level-set algorithm for propagating front curvature dependent detonation shock fronts in complex geometries[J]. Combustion Theory and Modelling, 2013, 17(1): 109-141.
[7]	张旭. 曲线坐标系中钝感炸药非理想爆轰波传播的Level Set 方法[D]. 绵阳: 中国工程物理研究院, 1999.
	ZHANG X. Level set method on non-ideal detonation of IHE in curvilinear coordinate[D]. Mianyang: China Academy of Engineering Physics, 1999. (in Chinese)
[8]	柏劲松, 李平, 钟敏, 等. 以DSD理论和LS方法为基础的程序燃烧法[J]. 爆炸与冲击, 2008, 28(5): 401-406.
	BAI J S, LI P, ZHONG M, et al. A program burn method based on detonation shock dynamics and level set (LS) methods[J]. Explosion and Shock Waves, 2008, 28(5): 401-406. (in Chinese)
[9]	姜洋, 钟敏, 孙承纬, 等. 非理想爆轰波阵面传播的Level Set方法应用研究[J]. 兵工学报, 2010, 31(7): 896-901.
	JIANG Y, ZHONG M, SUN C W, et al. Application of the level set method for propagation of non-ideal detonation wave[J]. Acta Armamentarii, 2010, 31(7): 896-901. (in Chinese)
[10]	钟敏. 三维非理想爆轰波阵面传播过程的数值方法和数值模拟[D]. 中国工程物理研究院, 2005.
	ZHONG M. The numerical method and simulation for propagating front of non-ideal 3D detonation[D]. Mianyang: China Academy of Engineering Physics, 2005. (in Chinese)
[11]	张莉, 吴开腾. 固定界面Level Set方法在爆轰波阵面传播中的应用[J]. 兵工学报, 2019, 40(10): 2080-2087.
	ZHANG L, WU K T. The Application of fixed-interface level set method in the calculation of detonation wavefront propagation[J]. Acta Armamentarii, 2019, 40(10): 2080-2087. (in Chinese)
[12]	谭多望, 方青, 张光升, 等. 常温下JB-9014钝感炸药的DSD参数研究[J]. 高压物理学报, 2009, 23(3): 161-166.
	TAN D W, FANG Q, ZHANG G S, et al. Detonationshock dynamics calibration of JB-9014 explosive at ambient temperature[J]. Chinese Journal of High Pressure Physics, 2009, 23(3): 161-166. (in Chinese)
[13]	姜洋, 黎源, 唐蜜, 等. 惰性介质约束下非理想爆轰波的传播[J]. 高压物理学报, 2013, 27(4): 599-603.
	JIANG Y, LI Y, TANG M, et al. Propagation of non-ideal detonation wave confined by inert medium[J]. Chinese Journal of High Pressure Physics, 2013, 27(4): 599-603. (in Chinese)
[14]	VOELKEL S J, ANDERSON E K, SHORT M, et al. Effect of lot microstructure variations on detonation performance of the triaminotrinitrobenzene (TATB)-based insensitive high explosive PBX 9502[J]. Combustion and Flame, 2022, 246: 112373.
[15]	ANDERSON E K, SHORT M, VOELKEL S J, et al. Experimental investigation of high explosive detonation structure and dynamics near the failure diameter[J]. Proceedings of the Combustion Institute, 2024, 40(1-4): 105320.
[16]	ANDREWS S A. Verification and validation of detonation-shock-dynamics relations for explosives described by general equation of state and chemical reaction models[J]. Combustion Theory and Modelling, 2024, 28(5): 554-578.
[17]	TANG K, PAN Z, DONG G. Understanding detonation wave dynamics in annular channels with geometric and pressure variations[J]. Proceedings of the Combustion Institute, 2024, 40(1-4): 105437.
[18]	ANDERSON E K, SHORT M, VOELKEL S J, et al. Influence of initial density on detonation propagation in a TATB-based high explosive[J]. Combustion and Flame, 2025, 273: 113920.
[19]	TARJAN R. Depth-first search and linear graph algorithms[J]. SIAM Journal on Computing, 1972, 1(2): 146-160.
[20]	GROPP W, LUSK E, SKJELLUM A. Using MPI: portable parallel programming with the message-passing-interface[M]. Cambridge, Massachusetts: The MIT Press, 2014.
[21]	HENDRICKSON B, PLIMPTON S J, et al. Finding strongly connected components in distributed graphs[J]. Journal of Parallel and Distributed Computing, 2005, 65(8): 901-910.
[22]	HONG S, RODIA N C, OLUKOTUN K. On fast parallel detection of strongly connected components (SCC) in small-world graphs[C]// Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis, Denver, US: IEEE, 2013.
[23]	陈江涛, 肖维, 赵炜, 等. 计算流体力学验证与确认研究进展[J]. 力学进展, 2023, 53(3): 626-660.
	CHEN J T, XIAO W, ZHAO W, et al. Advances in verification and validation in computational fluid dynamics[J]. Advances in Mechanics, 2023, 53(3): 626-660. (in Chinese)
[24]	THRUSSELL J, FERGUSON J M. ExactPack: a python library of exact analytic solutions[J]. SoftwareX, 2023, 24: 101560.
[25]	ISRAEL D M, DOEBLING S W, et al. ExactPack documentation[R]. LA-UR-16-23260, Los Alamos National Laboratory, 2016.
[26]	AIDA T, WALTER J W, ASLAM T D, et al. Verification of 2-D detonation shock dynamics in conjunction with Los Alamos Lagrangian hydrocode[R]. LA-UR-12-20792, Los Alamos National Laboratory, 2012.
[27]	LAMBERT D E, STEWART D S, YOO S, et al. Experimental validation of detonation shock dynamics in condensed explosives[J]. Journal of Fluid Mechanics, 2006, 546: 227-253.
[28]	TERRONES G, BURKETT M W, MORRIS C L. Burn front and reflected shock wave visualization in an inertially confined detonation of high explosive[C]// Proceedings of AIP Conference, Chicago, US: American Physical Society, 2012, 1426: 239.
[29]	HUGHES J M, TERRONES G, SHORES E F. Cyclops I:modeling error study for inertially confined detonation of insensitive high explosive (IHE) PBX-9502[R]. New Mexico, US: Los Alamos National Laboratory, 2018.
[30]	HODGSON A N. Modelling an IHE experiment with a suite of DSD models[C]// Proceedings of the 18th APS-SCCM and 24th AIPAPT, Washington, D.C., US: IOP Publishing, 2013.