基于SPH方法的3D高速侵彻并行数值模拟

doi:10.12382/bgxb.2025.0427

摘要/Abstract

摘要：

针对高速侵彻过程中涉及的大变形、损伤与断裂等复杂物理现象,基于光滑粒子流体动力学方法,开发了用于弹丸侵彻薄金属靶板的并行数值模拟方法。为准确描述材料在高速载荷作用下的力学响应,采用简化Johnson-Cook损伤模型。为解决SPH仿真中粒子数量剧增带来的高昂计算成本问题,将计算域划分为子域并将粒子信息在子域间传递,开发并实现了基于MPI的CPU并行求解器。将模拟结果与文献实验数据对比,对应8mm和10mm厚靶板的工况,预测的最大误差分别为7.86%和5.44%,验证了该数值方法在预测剩余速度和侵彻过程方面的精确性。对并行框架的加速性能进行了系统评估,该框架能显著提升计算效率,在处理一个包含约179万粒子的中等规模问题时,使用54个CPU核心可达到0.76的并行加速效率。该并行SPH框架在保证仿真精度的前提下,成功将计算能力扩展至更高量级,能够处理超过一亿个粒子的大规模仿真。

关键词: 高速侵彻, 光滑粒子流体动力学, CPU并行, 子域划分, 粒子迁移

Abstract:

Based on the Smoothed Particle Hydrodynamics (SPH) method, a parallel numerical simulation method was developed for projectile penetration into thin metal targets to address complex physical phenomena such as large deformation, damage, and fracture involved in high-velocity penetration. To accurately describe the material’s mechanical response under high-speed loading, a simplified Johnson-Cook damage model was adopted. To tackle the high computational cost caused by the rapid increase in particle numbers in SPH simulations, the computational domain was divided into subdomains, and an MPI-based CPU parallel solver was developed and implemented to exchange particle information between them. The accuracy of the numerical method in predicting residual velocity and the penetration process was validated by comparing the simulation results with experimental data from the literature. For the 8mm and 10mm thick target plates, the maximum prediction errors were 7.86% and 5.44%, respectively. A systematic evaluation of the parallel framework's acceleration performance showed a significant improvement in computational efficiency. For a medium-scale problem involving approximately 1.79 million particles, a parallel speedup efficiency of 0.76 was achieved using 54 CPU cores. While ensuring simulation accuracy, this parallel SPH framework successfully extends the computational capability to a higher order of magnitude, enabling large-scale simulations with over 100 million particles.

Key words: high-velocity penetration, smoothed particle hydrodynamics, CPU-based parallel computing, subdomain partitioning, particle migration

邓敏杰, 宋卫东, 肖李军. 基于SPH方法的3D高速侵彻并行数值模拟[J]. 兵工学报, 2025, 46(10): 250427-.

DENG Minjie, SONG Weidong, XIAO Lijun. Parallel Numerical Simulation of 3D High-Speed Penetration Based on the SPH Method[J]. Acta Armamentarii, 2025, 46(10): 250427-.

图/表 17

图1 粒子间相互作用

Fig.1 Particle-particle interaction

图2 子域划分示意图

Fig.2 Schematic diagram of subdomain partitioning

图3 Cell种类

Fig.3 Types of Cell

图4 粒子数据交换

Fig.4 Exchange of particles’ data

图5 粒子迁移

Fig.5 Migration of particles

图6 数值模型示意图

Fig.6 Schematic diagram of the numerical model

图7 粒子间距敏感性

Fig.7 Sensitivity of Δh

表1 动态负载平衡算法

Table 1 Dynamic load balancing algorithm

算法1:动态负载平衡算法
1.	if (负载不平衡度>阈值){
2.	ParMetis重新图划分,生成新Cube分配方案;
3.	计算需迁移的Cube列表;
4.	for每个目标进程in迁移目标列表{
5.	打包待发送Cube数据;
6.	MPI_Isend(数据大小,目标进程, tag1, &requests); }
7.	for每个源进程in迁移源列表{
8.	MPI_Irecv(接收数据大小,源进程, tag1, &requests); }
9.	MPI_Waitall(requests);
10.	for每个目标进程in迁移目标列表{
11.	MPI_Isend(实际数据,目标进程, tag2, &requests); }
12.	for每个源进程in迁移源列表{
13.	分配接收缓冲区(根据接收大小);
14.	MPI_Irecv(实际数据,源进程, tag2, &requests); }
15.	MPI_Waitall(requests); }

表2 仿真工况

Table 2 Simulation conditions

序号	v₀/(m·s^-1)	t/mm	序号	v₀/(m·s^-1)	t/mm
1	298.0	8	11	296.0	10
2	250.8	8	12	277.5	10
3	190.7	8	13	241.5	10
4	182.2	8	14	204.0	10
5	173.7	8	15	192.9	10
6	165.2	8	16	184.9	10
7	160.7	8	17	172.6	10
8	156.0	8	18	169.3	10
9	152.5	8	19	161.2	10
10	137.4	8	20	131.3	10

表3 Johnson-Cook本构模型参数

Table 3 Parameters of Johnson-Cook constitutive model

参数	靶板	弹丸
密度ρ/(kg·m^-3)	7850	7850
弹性模量E/GPa	200	205
泊松比ν	0.33	0.33
A/MPa	490	1900
B/MPa	807	0
n	0.73	0
C	0.0114	0
k	0.94	0

表4 Mie-Grüneisen状态方程参数

Table 4 Parameters of the Mie-Grüneisen equation of state

参数	靶板	弹丸
S_S	1.5	1.5
C_S/(m·s^-1)	5047	5110.25
γ	2	2

图8 圆柱形弹丸以初速190.7m/s侵彻靶板过程(穿透工况)

Fig.8 Penetration process of a cylindrical projectile into a target plate at an initial velocity of 190.7m/s(Perforation case)

图9 圆柱形弹丸以初速137.4m/s侵彻靶板过程(未击穿工况)

Fig.9 Penetration process of a cylindrical projectile into a target plate at an initial velocity of 137.4m/s(Non-perforation case)

图10 弹丸侵彻8mm厚靶板剩余速度

Fig.10 Residual velocity of the projectile after penetrating an 8mm thick target plate

图11 弹丸侵彻10mm厚靶板剩余速度

Fig.11 Residual velocity of the projectile after penetrating an 10mm thick target plate

图12 并行性能曲线

Fig.12 Curves of parallel performance

图13 弹丸侵彻靶板过程应力云图

Fig.13 Stress contour plot of the projectile’s penetration process into the target plate

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