刘君, 董海波, 张文昊. 化学非平衡解耦算法精度分析及其改进[J]. 空气动力学学报, 2018, 36(4): 634-641. DOI: 10.7638/kqdlxxb-2017.0083
引用本文: 刘君, 董海波, 张文昊. 化学非平衡解耦算法精度分析及其改进[J]. 空气动力学学报, 2018, 36(4): 634-641. DOI: 10.7638/kqdlxxb-2017.0083
LIU Jun, DONG Haibo, ZHANG Wenhao. Precision analysis and improvement of chemical non-equilibrium uncoupled method[J]. ACTA AERODYNAMICA SINICA, 2018, 36(4): 634-641. DOI: 10.7638/kqdlxxb-2017.0083
Citation: LIU Jun, DONG Haibo, ZHANG Wenhao. Precision analysis and improvement of chemical non-equilibrium uncoupled method[J]. ACTA AERODYNAMICA SINICA, 2018, 36(4): 634-641. DOI: 10.7638/kqdlxxb-2017.0083

化学非平衡解耦算法精度分析及其改进

Precision analysis and improvement of chemical non-equilibrium uncoupled method

  • 摘要: 模拟化学非平衡流问题涉及到流动方程和化学反应方程两部分的求解,流动方程组中包含所有组元的偏微分方程,导致求解变量成数量级增加,点隐算法和全隐算法在求解源项刚性问题时,通常会涉及到矩阵求逆运算,这些因素带来的巨大计算量限制了隐式算法在复杂工程问题中的应用。1993年刘君提出了化学非平衡流解耦算法,将控制方程组分解为流动和化学反应两部分,流动方程的求解采用冻结流假设来描述流体微团沿流线的运动过程,化学反应方程的求解描述流体微团在随体坐标系下发生绝热、定容的爆炸过程。结合解耦算法和有限体积法的特点对这种解耦算法进行改进,提出的优化算法不需要求解组元变量所对应的偏微分方程组,只求解由5个基本变量构成的,形式上与量热完全气体近似的偏微分方程组,通过对比计算结果发现优化算法可以显著地提高计算效率。同时,将精细积分方法应用于化学非平衡流问题的求解中,通过与传统的VODE方法和α-QSS方法对比发现,精细积分方法的鲁棒性更优、精度对时间步长不敏感,适当的选取时间步长,可以充分发挥精细积分方法的优势。

     

    Abstract: The numerical simulation of chemical non-equilibrium flow contains solving the governing equations of flow and chemical kinetics. Point-implicit and fully implicit methods, involving the matrix inversion calculations, require great computational costs in solving the stiff ordinary differential equations that limits their applications in complex engineering problems. To solve this problem, Liu proposed a novel uncoupled method for chemical non-equilibrium flow in 1993, the governing equations are decomposed into two parts of flow and chemical reaction. A frozen flow model is used in flow equations to describe the motion of fluid, and the solution of chemical reaction equations describe the explosion process in adiabatic and source equations are employed to simulate chemical reaction process in the local adiabatic and constant volume thermodynamic system. By combining Liu's uncoupled method with the space mean character of finite volume method, the present study introduces an optimization flow equation method, which only resolves the partial differential equations with five variables. These equations have the same form as calorically perfect gas equations. The optimization method can significantly improve the computational efficiency. In addition, the authors first use the precise time-integration method in solving the stiff ordinary differential equations. Compared with the VODE and α-QSS methods, the precise time-integration method has better numerical stability and is insensitive to time step. Therefore, the advantage of precise time-integration method on solving the stiff ordinary differential equations can be prominent by selecting a proper time step.

     

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