二维磁驱动数值模拟程序MDSC2的验证与确认

阚明先; 段书超; 张朝辉; 肖波; 王刚华; 王贵林; 冯春生; 彭洁

doi:10.11884/HPLPB201931.180300

二维磁驱动数值模拟程序MDSC2的验证与确认

doi: 10.11884/HPLPB201931.180300

1.
中国工程物理研究院流体物理研究所, 四川绵阳 621999
2.
湘潭大学数学与计算科学学院, 湖南湘潭 411105

基金项目:

国家自然科学基金项目 11405167

国家自然科学基金项目 11571293

详细信息

作者简介:
阚明先(1971—)，男，副研究员，研究方向为磁流体力学数值模拟；kanmx@caep.cn

中图分类号: O361.3
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- 被引次数: 0
出版历程
- 收稿日期: 2018-11-01
- 修回日期: 2019-03-01
- 刊出日期: 2019-07-15

Verification and validation of two dimensional magnetically driven simulation code MDSC2

1.
Institute of Fluid Physics, CAEP, P. O. Box 919-105, Mianyang 621999, China
2.
School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China

摘要

摘要: 为了对磁驱动实验提供高置信度的数值模拟，需要开展磁流体力学程序的验证与确认。采用人为解比较法、网格收敛性研究和与成熟程序比较等方法，对二维磁驱动数值模拟程序MDSC2进行了程序验证。数值模拟表明：MDSC2程序正确地表示了磁流体力学模型，其中热扩散、磁扩散的离散格式具有二阶收敛精度。采用与磁驱动实验相比较的方法，进行了MDSC2程序的确认。对聚龙一号装置上的PTS-061发次磁驱动单侧飞片发射和PTS-122发次磁驱动双侧飞片发射实验进行了模拟，模拟的飞片自由面速度与实验测量的飞片自由面速度相一致；对FP-1装置上的固体套筒实验进行了模拟，模拟的套筒内外半径与实验测量结果相一致。MDSC2程序能正确模拟磁驱动单侧飞片发射、磁驱动双侧飞片发射和磁驱动固体套筒等磁驱动实验。
- 二维磁驱动数值模拟程序 /
- 验证 /
- 确认 /
- 数值模拟
Abstract: Magneto-hydrodynamic (MHD) code has been widely used in the field of high current pulse technology, astrophysics and so on. Especially in recent years, with the rapid development of high pulse technology and magnetically driven experiments such as Z-pinch, magnetically driven flyer plate and magnetically driven quasi-isentropic/shock compression, experimental researchers and designers pay more and more attention to the correctness and reliability of MHD code. The verification and validation of the two dimensional magnetically driven simulation code MDSC2 is an important means to evaluate its correctness and reliability. In this paper, the MDSC2 code is verified by ways of comparison with artificial solutions, mesh convergence analysis and comparison with mature codes, and it is also validated by experiments, using magnetically driven one-sided flyer plate, magnetically driven two-sided flyer plates and magnetically driven solid liner. The numerical simulation shows that, the MDSC2 code not only correctly represents the MHD equations, but also can correctly simulate the magnetically driven experiments.
- two dimensional magnetically driven simulation code /
- verification /
- validation /
- numerical simulation

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图 1 热扩散模型求解域Ω的示意图

Figure 1. Domain of thermal diffusion module

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图 2 求解域Ω在xy平面上的投影图

Figure 2. Cross section of 3D domain Ω on xy plane

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图 3 初始猜测磁场为驱动源模拟的飞片自由面速度

Figure 3. Simulated velocity histories (initially guessed B field as driving source)

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图 4 优化磁场为驱动源模拟的飞片自由面速度

Figure 4. Simulated velocity histories (optimized B field as driving source)

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图 5 EHD程序和MDSC2程序模拟的80 ns时的速度分布图

Figure 5. Velocity distribution of flyer plate(EHD vs MDSC2)

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图 6 PTS-061发次实验的电流加载历史

Figure 6. Measured current history of shot PTS-061

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图 7 模拟的PTS-061发次实验的速度历史

Figure 7. Simulated and measured velocity histories of shot PTS-061

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图 8 PTS-122发次实验的电流加载历史

Figure 8. Measured current history of shot PTS-122

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图 9 模拟的PTS-122发次实验的速度历史

Figure 9. Simulated and measured velocity histories of shot PTS-122

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图 10 磁驱动铝套筒实验测量电流

Figure 10. Measured current history on FP-1

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图 11 模拟的铝套筒平均内外半径历史

Figure 11. Histories of inner and outer radius of liner

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表 1 MDSC2程序中热扩散离散格式的逼近性

Table 1. Approximation of the discrete scheme of thermal diffusion equation in MDSC2 code

α/(°)	32×32 grid		64×64 grid		128×128 grid		256×256 grid
α/(°)	error	rate	error	rate	error	rate	error	rate
0	6.40×10^-4	-	1.60×10^-5	4.0	4.00×10^-6	4.0	1.00×10^-6	4.0
30	3.89×10^-4	-	9.94×10^-5	3.9	2.52×10^-5	3.9	6.35×10^-6	4.0
60	1.70×10^-3	-	4.45×10^-4	3.8	1.14×10^-4	3.9	2.87×10^-5	4.0
80	1.80×10^-2	-	4.71×10^-3	3.8	1.20×10^-3	3.8	3.04×10^-4	4.0

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表 2 MDSC2程序中磁扩散方程离散格式的逼近性

Table 2. Approximation of the discrete scheme of magnetic diffusion equation in MDSC2 code

α/(°)	32×32 grid		64×64 grid		128×128 grid		256×256 grid
α/(°)	error	rate	error	rate	error	rate	error	rate
0	1.90×10^-4	-	4.74×10^-5	4.0	1.19×10^-5	4.0	2.97×10^-6	4.0
30	2.60×10^-4	-	6.61×10^-5	3.9	1.67×10^-5	4.0	4.20×10^-6	4.0
60	4.93×10^-4	-	1.29×10^-4	3.8	3.31×10^-5	3.9	8.39×10^-6	3.9
80	1.60×10^-3	-	4.36×10^-4	3.7	1.14×10^-4	3.8	2.94×10^-5	3.9

下载: 导出CSV

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