Development of Compressible Flow Equations into Incompressible Environmental Flow Simulations

本研究将可压缩的Navier-Stokes方程推广到不可压缩的环境流动模拟中。首先，证明了低马赫数的可压缩解与试验问题的不可压缩解具有很好的一致性。并将该方法应用于二维和三维均匀各向同性湍流。为了保证高阶空间和时间精度，采用改进的微分正交（MDQ）方法对空间导数进行离散化，得到的常微分方程组在时间上采用四阶龙格-库塔格式进行积分。在这种情况下，流场中出现非物理振荡。然后，采用位移通量技术，得到了无非物理振荡的非常光滑的流场。与基于高阶有限差分法和谱法的不可压缩解相比，本文的结果显示出了更好的流场和统计量，即总能量、能量耗散、熵耗散和能谱。其次，将不可压缩气流作为具有密度分层的基本环境模拟。在层流区，存在弱密度分层的解与相应的不可压缩解具有很好的一致性。然而，在强密度分层中，本方法给出的解仅与定性一致。在此基础上，引入了马赫数均压修正方法，并在具有圆形凸起的二维通道流中进行了验证。与通常基于密度的可压缩解相比，在超声速到亚声速流动范围内得到了很好的一致性。在拟不可压缩区域，Ma<0.01，通常的可压缩解与目前的解不同。然而，目前的解与不可压缩解几乎相同。因此，本文提出的马赫均压修正方法对于不可压缩流动的数值模拟是很有前景的。少

In this research, the compressible Navier-Stokes equations are developed into the incompressible environmental flow simulations. First, it is shown that the compressible solutions with low Mach number are in very good agreement with the incompressible solutions in the test problem. And the present approach is applied to two and three dimensional homogeneous isotropic turbulence. In order to ensure the higher order spatial and time accuracy, the spatial derivatives are discretized by the modified differential quadrature (MDQ) method and the resulting system of ordinary differential equations in time is integrated by the 4th order Runge-Kutta scheme. In these cases, the unphysical oscillations appear in the flow field. Then, the shifted flux technique is adopted, so that the very smooth flow field without unphysical oscillations can be obtained. In comparison with the incompressible solutions based on higher order finite difference and spectral method, the present results show the excell … More ent flow field and statistical quantities, i.e., total energy, energy dissipation, enstrophy dissipation and energy spectra.Next, the incompressible flows over a hill are considered as the fundamental environmental simulation with density stratification. In the laminar flow region, the present solutions with weak density stratification are in very good agreement with the corresponding incompressible solution. However, in the strong density stratification, the present approach gives the solutions with only qualitative agreement. Then, we introduce the Mach uniform pressure correction method and the validations are performed in the two dimensional channel flow with circular bump. In comparison with the usual compressible solutions based on the density, the very good agreement can be obtained in the range from supersonic flow to subsonic flow. In the quasi-incompressible regime, Ma<0.01, the usual compressible solutions are different from the present solutions. However, the present solutions are almost the same as the incompressible solutions. Therefore, it is concluded that the present Mach uniform pressure correction approach is very promising for numerical simulation of incompressible flows. Less