松弛方法在计算凝聚炸药爆轰问题中的应用

陈秋阳; 于明

doi:10.11883/1001-1455(2015)06-0785-07

摘要: 利用松弛近似，将非线性的凝聚炸药爆轰控制方程转化为线性的松弛方程组，并采用五阶WENO格式和五阶线性多步显隐格式对线性松弛方程组进行空间方向和时间方向的离散，由此建立具有高精度和高分辨率性质的计算凝聚炸药爆轰的松弛方法。建立的松弛方法可以避免求解Riemann问题及计算非线性通量的Jacobi矩阵，同时无需分裂处理反应源项。通过对凝聚炸药的平面一维定常爆轰波结构及球面一维聚心、散心爆轰起爆和传播过程的数值模拟，验证了所建立的松弛方法能够很好地计算凝聚炸药爆轰问题。

关键词:

Abstract: Based on the theory of relaxation approximation, the nonlinear governing equations of detonation in condensed explosives are transformed into linear relaxation systems, which can easily adopt simple and effective high resolution scheme. A fifth-order WENO reconstruction scheme in spatial discretization and a fifth-order IMEX scheme of linear multistep methods with monotonicity and TVB in time discrtiezation are utilized, where it can leave out solving Riemann problem and computing the Jacobian matrix of the nonlinear flux, and make it unnecessary to split the stiff source term resulting from the chemical reaction. The developed method is applied to simulating the steady structure of one-dimensional planar detonation wave and unsteady initiation and propagation of one-dimensional spherically convergent and divergent detonation wave in condensed explosives PBX9404, with the results demonstrating the excellent performance of the present method.

Key words:

图 1 PBX9404炸药化学反应区内物理量分布

Figure 1. Distrubitions of physical variables in chemical reaction zone of PBX9404

下载: 全尺寸图片幻灯片

图 2 PBX9404炸药CJ爆速和Von Neumann压力与离散网格尺度的关系

Figure 2. Relations of the CJ velocity and Von Neumann pressure to the mesh sizes in PBX9404

下载: 全尺寸图片幻灯片

图 3 PBX9404炸药平面爆轰波传播过程中压力和速度分布变化趋势

Figure 3. Distributions of pressure and velocity of planar detonation wave in PBX9404

下载: 全尺寸图片幻灯片

图 4 PBX9404炸药球面聚心爆轰波传播过程中压力和速度分布变化趋势

Figure 4. Distributions of pressure and velocity of spherically convergent detonation wave in PBX9404

下载: 全尺寸图片幻灯片

图 5 PBX9404炸药球面散心爆轰波传播过程中压力和速度分布变化趋势

Figure 5. Distributions of pressure and velocity of spherically divergent detonation wave in PBX9404

下载: 全尺寸图片幻灯片

[1]	Mader C L. Numerical modeling of explosives and propellants[M]. 2nd ed. New York: CRC Press, 1998.
[2]	Henshaw W D, Schwedeman D W. An adaptive numerical scheme for high-speed reactive flow on overlapping grids[J]. Journal of Computational Physics, 2003, 19(2): 420-447. https://www.sciencedirect.com/science/article/pii/S0021999103003231
[3]	Kapila A K, Schwedeman D W, Bdzil J B. A study of detonation diffraction in the ignition-and-growth model[J]. Combustion Theory and Modeling, 2007(11): 781-822. https://www.researchgate.net/publication/245326055_Study_of_detonation_diffraction_in_the_ignition-and-growth_model
[4]	Banks J W, Schwedeman D W, Kapila A K. A study of detonation propagation and diffraction with compliant confinement[R]. UCRL-JRNL-233735, 2007.
[5]	Schwedeman D W, Kapila A K, Henshaw W D. A study of detonation diffraction and failure for a model of compressible reactive flow[R]. UCRL-JRNL-M43735, 2010.
[6]	Yee H C, Kotov D V, Sjogreen B. Numerical dissipation and wrong propagation speed of discontinuties for stiff source terms[C]∥Proceedings of ICCFD. Hawaii, 2011.
[7]	Yee H C, Kotov D V, Shu C W. Spurious behavior of shock-capturing methods: Problems containing stiff source terms and discontuities[C]∥Proceedings of ICCFD7, 2012.
[8]	孙承纬, 卫玉章, 周之奎.应用爆轰物理[M].北京: 国防工业出版社, 2000.
[9]	Hundsdorfer W, Ruuth S J. IMEX extensions of linear multistep methods with general monotonicity and boundedness properties[J]. Journal of Computational Physics, 2007(225): 2016-2042. https://www.sciencedirect.com/science/article/pii/S0021999107001003
[10]	Liu T P. Hyperbolic conservation laws with relaxation[J]. Communications in Mathematical Physics, 1987(108): 153-175. doi: 10.1007/BF01210707
[11]	Jin S, Xin Z. The relaxation schemes for systems of conservation laws in arbitrary space dimensions[J]. Communications of Pure and Applied Mathematics, 1995(48): 235-276. doi: 10.1002/cpa.3160480303/full
[12]	Chalabi A. Convergence of relaxation schemes for hyperbolic conservation laws with stiff source[J]. Mathematics of Computation, 1999(68): 955-970.
[13]	Tang T. Convergence of MUSCL relaxing scheme to the relaxed scheme for conservation laws with stiff source terms[J]. Journal of Scientific Computing, 2000, 15(2): 173-195. doi: 10.1023/A:1007681726414
[14]	Henrick A K, Aslam T D, Powers J M. Mapped weighted essentially non-oscillatory schemes: Achieving optimal order near critical points[J]. Journal of Computational Physics, 2005(207): 542-567. https://www.sciencedirect.com/science/article/pii/S0021999105000409

期刊类型引用(0)

其他类型引用(1)