Non-intrusive polynomial chaos methods and its application in the parameters assessment of explosion product JWL
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摘要: 介绍了非嵌入多项式混沌法的数学模型，给出了非嵌入式多项式混沌法进行不确定度量化的主要步骤。采用此方法研究了平面、散心爆轰问题数值模拟中, JWL模型参数R1、R2服从均匀分布的随机变量时所引起的爆轰过程计算结果的不确度性，着重分析了爆轰传播过程中压力与密度的统计特性。研究结果表明，非嵌入式多项式混沌法可以为模型输入参数不确定性的传播对输出结果响应量的影响建立一种有效不确定度评估方法，为使用JWL模型时选取参数提供参考。
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关键词:
- 爆炸力学 /
- JWL状态方程 /
- 参数选取 /
- 非嵌入式多项式混沌法 /
- 不确定度量化
Abstract: A non-intrusive polynomial chaos method was introduced, and the main procedure of uncertainty quantification for JWL-EOS parameters was given. The method was implemented for the uncertainty quantification of the input parametersR1 and R2 of JWL-EOS to the detonation of plane and divergence. The results show that the methods of non-intrusive polynomial chaos can provide a valuable tool for the simulation of propagation of uncertainties, and uncertainty quantification for modeling and simulation in complex engineering. -
图 2 R1=4.8±0.5和R2=1.95±0.5随机抽样下物理量的期望和方差
Figure 2. Expectation and variance under the random-sample with R1=4.8±0.5 and R2=1.95±0.5
图 3 R1=7.3±0.5和R2=2.46±0.5随机抽样下物理量的期望和方差
Figure 3. Expectation and variance under the random-sample R1=7.3±0.5 and R2=2.46±0.5
图 5 R1=4.8±0.5和R2=1.95±0.5随机抽样下物理量的期望和方差
Figure 5. Expectation and variance under the random-sample R1=4.8±0.5 and R2=1.95±0.5
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[1] Green L, Lee E, Mitchell A, et al, Equations of state of PBX-9404, LX-07, RX-26-AF detonation products at pressure above detonation pressure[R]. UCRL-89664.1983. [2] 王瑞利, 张树道, 刘全, 等.复杂工程M & S中不确定度量化方法进展[C]//中国力学大会2013年论文摘要集.西安, 2013. [3] Wiener S. The homogeneous chaos[J]. America Journal of Mathematic, 1938, 60(4): 897-936. [4] Maitre P O, Knio O M. Spectral methods for uncertainty quantification: With applications to computational fluid dynamics[M]. New York: Springer, 2010. [5] Hosder S, Perez R, Walters R W. A non-intrusive polynomial chaos method for uncertainty propagation in CFD simulations[C]//44th AIAA Aerospace Sciences Meeting and Exhibit(2006). Reno, Nedava, 2006: 1-19. [6] Knio O, Maitre O. Uncertainty propagation in CFD using polynomial chaos decomposition[J]. Fluid Dynamics Research, 2006, 38: 616-640. [7] 王晓东, 康顺.多项式混沌法求解随机Burgers方程[J].工程热物理学报, 2010, 31(3): 393-398.Wang Xiao-dong, Kang Shun. Solving stochastic Burgers equation using polynomial chaos decomposition[J]. Journal of Engineering Thermophysics, 2010, 31(3): 393-398. [8] 刘智益, 王晓东, 康顺.多项式混沌方法在随机方腔流动模拟中的应用[J].工程热物理学报, 2012, 33(3): 419-422.Liu Zhi-yi, Wang Xiao-dong, Kang Shun. Application of multi-dimensional polynomial chaos on numerical simulation of stochastic cavity flow[J]. Journal of Engineering Thermophysics, 2012, 33(3): 419-422. [9] 刘全, 王瑞利, 林忠, 等.流体力学拉氏程序收敛性及数值计算不确定度初探[J].计算物理, 2013, 30(3): 346-352.Liu Quan, Wang Rui-li, Lin Zhong, et al. Asymptotic convergence analysis and quantification of uncertainty in Lagrangian computations[J]. Chinese Journal of Computational Physics, 2013, 30(3): 346-352. [10] 王瑞利, 林忠, 闫伟.多介质问题分析的前处理程序PreGenGrid[J].应用数学和力学, 2013, 5(15): 535-545.Wang Rui-li, Lin Zhong, Yan Wei. Simulations of the multi-medium problem pre-process: PreGenGrid[J]. Applied Mathematics and Mechanics, 2013, 5(15): 535-545. [11] 王瑞利, 林忠, 倪国喜.基于任意多边形拉氏网格的有限体积方法研究及应用[J].数值计算与计算机应用, 2006, 27(1): 31-38.Wang Rui-li, Lin Zhong, Ni Guo-xi. Base on arbitrary n-polygon Lagrange grids finite volume method and applications[J]. Journal of Numerical Methods and Computer Applications, 2006, 27(1): 31-38. -
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