Deterministic numerical simulation of non-linear neutron transport in inertial confinement fusion
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摘要: 从几个方面着手提高确定论方法的计算精度：首先，中子输运计算的相空间离散采用间断有限元处理方法，并使用较大的角度离散数和散射阶数；其次，使用蒙特卡罗直接统计方法得到高精度多群截面；最后，引入收敛于真解的中子-中子碰撞源迭代。数值算例验证表明，经过改进的确定论方法具有良好的稳定性和精度，能以可靠的精度求解考虑中子-中子碰撞过程的非线性问题。Abstract: Extremely high density neutrons could be produced in inertial confinement fusion, therefore the neutron-neutron collision process can no longer be neglected, especially that it leads to production of super-high energy neutrons of important value for diagnosis technique. For numerical simulation of neutron-neutron collision, Monte Carlo methods generally suffer from low efficiency, while deterministic methods have limited accuracy. In this paper, several measures are taken to improve the accuracy of deterministic method: Firstly, the phase space discretization of neutron transport calculation adopts discontinuous finite element method, and the numbers of angle discretization and the scattering order are relatively large; Secondly, direct Monte Carlo tallying method is used to obtain highly accurate multi-group cross sections; thirdly, a neutron-neutron collision source iteration method that converges to real solution is introduced. At last, numerical verification shows that the enhanced deterministic method has favorable stability and accuracy, the non-linear problem arise from consideration of neutron-neutron collision process can be solved with reliable accuracy.
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图 5 考虑n-n碰撞的多群固定源问题计算流程
Figure 5. Flow diagram of multi-group fixed source calculation with consideration of n-n collision
图 7 模型1 OpenMC和SN(p0, p1, p3, p5)D-T混合物区域75群通量计算结果和偏差
Figure 7. Calculation results and discrepancies of 75-group flux in D-T mixture region of model 1 between OpenMC and SN (p0, p1, p3, p5)
图 8 模型1 OpenMC和SN(p0, p1, p3, p5)Au区域75群通量计算结果和偏差
Figure 8. Calculation results and discrepancies of 75-group flux in Au region of model 1 between OpenMC and SN (p0, p1, p3, p5)
图 9 模型2 OpenMC和SN(p0, p1, p3, p5)D-T混合物区域75群通量计算结果和偏差
Figure 9. Calculation results and discrepancies of 75-group flux in D-T mixture region of model 2 between OpenMC and SN (p0, p1, p3, p5)
图 10 模型2 OpenMC和SN(p0, p1, p3, p5)CH区域75群通量计算结果和偏差
Figure 10. Calculation results and discrepancies of 75-group flux in CH region of model 2 between OpenMC and SN (p0, p1, p3, p5)
表 1 计算模型1源强1×1024 cm-3·sr-1·μs-1时外边界中子流
Table 1. Neutron current at outer surface while source strength is 1×1024 cm-3·sr-1·μs-1 in calculation model 1
group energy /MeV neutron current by DSMC/μs-1 neutron current by SN/μs-1 no n-n collision considering n-n collision no n-n collision considering n-n collision 0.0~7.0 8.276 85×1024 8.281 66×1024 7.017 50×1024 7.021 88×1024 7.0~10.0 1.916 48×1024 1.921 49×1024 2.033 06×1024 2.039 41×1024 10.0~14.0 6.718 30×1024 6.719 31×1024 7.073 58×1024 7.077 15×1024 14.0~14.2 3.855 91×1025 3.853 08×1025 3.921 67×1025 3.919 16×1025 14.2~14.7 0.0 7.439 90×1020 0.0 8.055 19×1020 14.7~15.5 0.0 9.857 80×1020 0.0 1.079 21×1021 15.5~16.5 0.0 1.101 48×1021 0.0 1.173 97×1021 16.5~18.0 0.0 1.466 80×1021 0.0 1.540 64×1021 18.0~20.0 0.0 1.624 20×1021 0.0 1.771 08×1021 20.0~22.0 0.0 1.366 84×1021 0.0 1.509 10×1021 22.0~24.0 0.0 1.071 23×1021 0.0 1.181 52×1021 24.0~26.0 0.0 7.428 90×1020 0.0 8.790 52×1020 26.0~28.0 0.0 3.844 26×1020 0.0 5.010 62×1020 28.0~30.0 0.0 1.384 33×1019 0.0 2.373 02×1017 total 5.547 07×1025 5.546 28×1025 5.534 09×1025 5.534 05×1025 
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表 2 计算模型1源强5×1024 cm-3sr-1 μs-1时外边界中子流
Table 2. Neutron current at outer surface while source strength is 5×1024 cm-3sr-1 μs-1 in calculation model 1
group energy /MeV neutron current by DSMC/μs-1 neutron current by SN/μs-1 no n-n collision considering n-n collision no n-n collision considering n-n collision 0.0~7.0 4.138 12×1025 4.119 92×1025 3.508 75×1025 3.519 62×1025 7.0~10.0 9.582 40×1024 9.790 89×1024 1.016 53×1025 1.032 11×1025 10.0~14.0 3.359 15×1025 3.378 30×1025 3.536 79×1025 3.545 47×1025 14.0~14.2 1.927 96×1026 1.921 22×1026 1.960 84×1026 1.954 63×1026 14.2~14.7 0.0 2.057 55×1022 0.0 2.013 55×1022 14.7~15.5 0.0 2.697 98×1022 0.0 2.697 08×1022 15.5~16.5 0.0 2.933 61×1022 0.0 2.932 84×1022 16.5~18.0 0.0 3.785 97×1022 0.0 3.846 71×1022 18.0~20.0 0.0 4.165 58×1022 0.0 4.419 02×1022 20.0~22.0 0.0 3.405 78×1022 0.0 3.762 61×1022 22.0~24.0 0.0 2.707 68×1022 0.0 2.944 32×1022 24.0~26.0 0.0 1.884 99×1022 0.0 2.189 96×1022 26.0~28.0 0.0 9.793 35×1021 0.0 1.248 77×1022 28.0~30.0 0.0 3.104 26×1020 0.0 2.954 76×1019 total 2.773 54×1026 2.771 42×1026 2.767 04×1026 2.766 95×1026
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表 3 计算模型2外边界中子流
Table 3. Neutron current at outer surface in calculation model 2
group energy /MeV neutron current at low source strength neutron current at high source strength no n-n collision considering n-n collision no n-n collision considering n-n collision 0.0~7.0 3.560 28×1019 3.560 29×1019 1.780 14×1020 1.780 16×1020 7.0~10.0 1.219 35×1019 1.219 36×1019 6.096 74×1019 6.096 95×1019 10.0~14.0 4.240 49×1019 4.240 50×1019 2.120 25×1020 2.120 26×1020 14.0~14.2 2.762 72×1020 2.762 72×1020 1.381 36×1021 1.381 35×1021 14.2~14.7 1.124 17×1014 1.255 78×1014 5.620 83×1014 8.911 26×1014 14.7~15.5 4.328 38×107 1.862 36×1013 2.164 19×108 4.655 89×1014 15.5~16.5 0.0 2.079 18×1013 0.0 5.197 93×1014 16.5~18.0 0.0 2.775 46×1013 0.0 6.938 63×1014 18.0~20.0 0.0 3.234 29×1013 0.0 8.085 69×1014 20.0~22.0 0.0 2.777 12×1013 0.0 6.942 75×1014 22.0~24.0 0.0 2.193 69×1013 0.0 5.484 20×1014 24.0~26.0 0.0 1.641 45×1013 0.0 4.103 60×1014 26.0~28.0 0.0 9.451 34×1012 0.0 2.362 82×1014 28.0~30.0 0.0 1.026 85×107 0.0 1.268 03×109 total 3.664 73×1020 3.664 74×1020 1.832 37×1021 1.832 37×1020
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