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在跨流域复杂流动问题的模拟中, 基于求解速度分布函数演化方程的气体动理论方法的效率问题一直受到工程应用领域关注. 研究提升气体动理论方法在定常流动模拟中的计算效率具有重要意义. 为了提升定常流动计算收敛速度, 本文提出了一种耦合宏观方程数值本构关系的气体动理论加速收敛方法. 通过求解Boltzmann模型方程, 将应力、热流高阶项的数值解与宏观方程耦合, 实现了宏观方程的封闭; 另一方面, 宏观方程的计算结果被用来更新Boltzmann模型方程的当地平衡态速度分布函数中的宏观物理量, 以此构造求解Boltzmann模型方程的全隐式数值格式. 通过跨流域方腔流动、超声速圆柱绕流及双圆柱干扰绕流案例的数值模拟, 对方法进行了广泛考核. 计算结果与常规气体动理论统一算法、直接模拟蒙特卡罗法符合良好, 证明该方法很好地描述了稀薄流动中的非线性本构关系, 以及激波、强壁面剪切、流动分离等强非平衡特征. 进一步, 对于低努森数 Kn的流动, 方法能显著加速收敛过程, 提升计算效率; 随着努森数 Kn增加, 气体对流输运效应减弱, 方法的加速收敛效果降低. 与此同时, 如何减少内迭代耗时, 进一步提升效率有待更多研究.
In the simulation of complex multi-scale flows covering various flow regimes, the computational efficiency of gas kinetic method by which the evolution equation of velocity distribution function is solved directly is the key to engineering applications. In order to accelerate simulation for steady flows, a gas kinetic algorithm accelerated by utilizing the macroscopic conservative equations with a digital constitutive relation is developed. In this algorithm, the contribution of the high-order terms of stress and heat flux in macroscopic conservative equations is determined by the gas kinetic solution. Meanwhile, the solution of the macroscopic conservative equations provides the macroscopic quantities for the equilibrium distribution function in the Boltzmann model equation, where a fully implicit scheme to solve the Boltzmann model equation is developed. Extensive validations are performed for the cavity flow, the supersonic flow around the cylinder, and the interactive rarefied flow around two side-by-side cylinders. The results from the above method are in good agreement with the results from the conventional gas kinetic unified algorithm and the direct simulation Monte Carlo method. It can be concluded that the nonlinear constitutive relation of rarefied flow can be well captured by the present method. And the ability of this method to simulate complex flows such as shock wave, strong wall shear and flow separation is demonstrated. Furthermore, the present method has shown to be much faster than the conventional gas kinetic unified algorithm, especially for the low- Knflows. As the value of Knincreases, the acceleration rate decreases, because the effect of flow convection becomes weak. Meanwhile, more effort is needed to reduce inner loop iterations to improve its efficiency. -
Keywords:
- gas kinetic unified algorithm/
- constitutive relation/
- convergence accelerated method/
- coupled method
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Kn 迭代步数(收敛标准: 10–7) 加速比 GKUA Coupled 0.010 8000 170 47.00 0.075 2300 300 7.60 1.000 1200 1100 1.09 
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