三维高超声速流动问题的高效数值方法及应用

在航空航天领域，高超声速流动问题的计算具有重要的科学工程意义。由于涉及激波、剪切层、黏性和湍流的相互作用，模拟高超声速流动问题要求数值格式能够准确稳定地捕捉复杂的流场结构。许多流行的数值格式(如CFD工业软件中普遍使用的Roe格式)在计算强激波时会遭遇不同形式的数值不稳定现象，这些非物理现象极大地影响了数值模拟结果的可靠性。本项目针对当前通量格式的不足，研究用于高超声速流动问题计算的低耗散、强稳定的三维通量格式。(1) 基于角点通量模型构造真正三维格式。由于同时考虑了界面法向和横向的信息，真正三维格式比传统上按维度分裂构造的高维格式具有更高的分辨率和稳定性。(2) 基于格式的耗散机理，分别利用耗散控制方法和代数方法改善其激波数值稳定性和提高线性波的分辨率。格式将被嵌入于OpenFOAM中并计算一些复杂的高超声速流动问题，如多组分化学反应流问题等，以便验证它们的应用能力。

In the field of aerospace, the calculation of hypersonic flows has important science and engineering significance. Due to the interaction of the shock waves, the shear layers, the viscosity and the turbulence, the numerical scheme is required to accurately and stably capture various complex flow structures in hypersonic flows. Many popular numerical schemes, such as the Roe scheme commonly used in CFD industrial software, will encounter different forms of numerical instability when capturing the strong shock waves. Those non-physical phenomena severely affect the reliability of numerical simulation results. In view of the shortcomings of current flux schemes, this project develops the three-dimensional flux schemes with low dissipation and strong stability. (1) The genuine 3D schemes are constructed based on the corner flux model. Since the information travelling along the normal and transversal directions is considered at the same time, the genuine 3D schemes have higher resolution and stability than the traditional three-dimensional schemes constructed by the dimension splitting. (2) Based on the dissipation mechanism of the numerical schemes, the method of dissipation control is employed to improve the shock numerical stability and the algebraic method is used to improve the resolution for linear waves. In order to demonstrate the ability of the scheme's application to practical problems, our schemes will be implemented into the free open-source software OpenFOAM to calculate some complex hypersonic flow problems, including the multi-component chemical reaction flows etc.