Confidence level of numerical simulation of detonation through quantifying the horsetail of error
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摘要: 针对爆轰流体力学数值模拟过程中输入参数的不确定性, 通过抽样技术, 形成确定性爆轰流体力学程序的各种输入和数值求解, 建立输入参数与输出响应量的样本, 再通过概率框架下的误差累积分布函数与马尾图, 给出了爆轰数值模拟过程中输入参数不确定度对模拟结果影响的置信度量化方法。通过一维黎曼问题、平面爆轰问题计算了误差马尾图, 给出了二维爆轰拉氏自适应流体动力学LAD2D程序计算网格与模拟结果置信度的关系, 对多物理爆轰过程发展高置信度数值模拟软件有很好的借鉴作用。Abstract: In the present study, sampling technique was used to deal with the input parameter uncertainty in the numerical simulation of detonation CFD(computational fluid dynamics). Then the deterministic detonation CFD program was constructed with different input. The sample of the input parameter and system response quantity was obtained through the previous result. The cumulative distribution function and the horsetail of error was utilized to achieve the confidence level, which was then used to assess the influence of the input parameter uncertainty on the simulation result of detonation CFD. The horsetail graph of error in one dimensional Riemann problem and planar detonation problem were presented to analyze the relationship between the confidence level of simulation result and the mesh used in LAD2D. This method provides a reference for developing the software of multi-physics detonation process on high confidence level.
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图 1 网格尺度0.1~0.025(16套)时计算结果与解析解的对比
Figure 1. Comparison between numerical results and analytic solutionsfor different mesh scales of 0.1~0.025(16 sets mesh)
图 2 网格尺度0.1~0.025(16套)计算结果与解析解的对比误差统计分析的马尾图
Figure 2. Horsetail figure of error between numerical results and analytic solutions for different mesh scales of 0.1~0.025(16 sets mesh)
图 3 网格尺度0.04~0.025(14套)时计算结果与解析解的对比误差统计分析的马尾图
Figure 3. Horsetail figure of error between numerical results and analytic solutions for different mesh scales of 0.1~0.025(14 sets mesh)
图 4 网格尺度0.1~0.01(10套)时不同时刻计算结果误差统计分析的马尾图
Figure 4. Horsetail figure of error between numerical results and analytic solutions at different times
图 5 4套参数在不同网格尺度下的计算结果误差统计分析的马尾图(t=8 μs)
Figure 5. Horsetail figure of error with four sets parameters for different mesh scales(t=8 μs)
表 1 JWL状态方程4套参数
Table 1. Four sets of parameters for JWL state eqution
参数代号 A/GPa B/GPa R1 R2 ω PAP1 765.788 14.249 4.3 1.45 0.28 PAP2 947.774 59.206 5.0 2.00 0.28 PAP2 1 502.851 134.913 6.3 2.40 0.28 PAP3 3 250.433 233.271 8.2 2.80 0.28 
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