双原子分子气体的定常隐式全流域多尺度算法

巨大的计算资源需求极大地阻碍了统一气体动理学格式的应用。采用宏观预估技术,基于Boltzmann-Rykov模型方程发展全流域适用的保守恒定常隐式算法,协同求解宏观方程和微观方程以加速收敛。在单元界面,通过模型方程特征差分解构造简单高效的多尺度数值通量,并结合非均匀非结构速度空间和速度空间自适应技术进一步降低计算需求、提升计算效率。超声速和高超声速平板绕流和圆球绕流的数值结果验证了算法的准确性与高效性。结果表明,算法能够准确求解二维和三维双原子气体多尺度流动问题,且相比于显式离散统一气体动理学格式可加速一个量级。

Multi-scale implicit scheme for steady flows of diatomic molecular gases in all flow regimes

The application of unified gas kinetic scheme is greatly hindered by the huge requirements of computing resources. Based on Boltzmann-Rykov model equation, a conservative implicit scheme for steady flows in all flow regimes was developed by adopting macroscopic prediction technique, and the macroscopic equation and microscopic equation were solved collaboratively to accelerate the convergence. At the cell interface, a simplified and efficient multi-scale numerical flux was directly constructed from the characteristic difference solution of kinetic model equation. The adoption of non-uniform, unstructured velocity space and velocity space adaptive technology further reduce the requirement of computation and improve computational efficiency. The applications of unstructured discrete velocity space and adaptive discrete velocity space reduced the number of velocity mesh significantly and made the present method be rather efficient. The accuracy and effectiveness of the proposed method were confirmed by the simulations of rarefied supersonic and hypersonic flows over a flat plate, supersonic and hypersonic flows over a sphere. Numerical results indicate that the proposed method can accurately solve two-dimensional and three-dimensional diatomic gas multi-scale flow problems, and it is about one orders of magnitude faster than the explicit discrete unified gas kinetic scheme method.