Application of relaxation method for calculating detonation in condensed explosives
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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。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.
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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
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
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
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
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