An Improved Efficient Parallel DSD Algorithm and Its Verification & Validation

doi:10.12382/bgxb.2025.0411

Abstract

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

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-.

Figures/Tables 25

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

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

Fig.3 Example of boundary node with multiple stencil candidates

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

Fig.5 Schematic diagram of 2D domain decomposition

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

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

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

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

Fig.9 Configuration of the rate stick detonation problem

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

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

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

Fig.12 Configuration of the explosive arc detonation problem

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

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

Fig.15 Assembly sketch for DSD Passover validation experiment

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°

Fig.16 Results of simulation

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

Fig.18 Cross-section schematic of the Cyclops experiment

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°

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

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

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

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