可压湍流的直接数值模拟

The compressible turbulent flow is an important physical phenomenon in many applications. Understanding of turbulence is a key for solving practical problems. The main characteristic of turbulence is strong interaction between the unsteady multi-scale structures. This kind of problems is difficult to be solved if only with the traditional methods. The direct numerical simulation is an important means for solving turbulent flow problems. In present subject the relation between the physical scales and accuracy of methods are analyzed. The constructed fifth order accurate upwind compact scheme and the super compact scheme with arbitrary high order accuracy are further improved. For capturing the unsteady shocklets are developed upwind compact scheme with group velocity control(GVC) and eighth order accurate GVC8 scheme. These high order accurate schemes with high resolution are used to simulate the complex flow fields such as the incompressible and compressible turbulent channel flows, the compressible homogeneous isotropic turbulence, the jet flow, and the compressible mixing layers. The complete flow process is presented from flow instability, formation of coherent structures to transition to turbulence. The first dada base for studying the compressible turbulence in China is established. Present research provides method and theoretic base for understanding and control of compressible turbulence.

针对可压缩湍流的物理特征，构造既能对三维非定常激波具有高分辨能力，又能正确模拟小尺度物理量的高精度计算方法。用于求解三维非定常可压缩NS方程，直接数值模拟平面槽道湍流和平面混合湍流，研究可压湍流非定常物理机理、压缩效应和非定常激波对湍流结构的影响。为可压湍流的直接数值模拟提供有效的计算方法；为湍流的控制提供可靠依据。