Development of Compressible Flow Equations into Incompressible Environmental Flow Simulations

本研究将可压缩Navier-Stokes方程发展为不可压缩环境流动模拟。首先，它表明，在低马赫数的可压缩的解决方案是非常好的协议与不可压缩的解决方案在测试问题。并将该方法应用于二维和三维均匀各向同性湍流。为了保证更高的空间和时间精度，空间导数离散的修正微分求积（MDQ）方法和所得到的常微分方程组的时间是由四阶龙格-库塔格式积分。在这些情况下，流场出现非物理振荡。然后，采用位移通量技术，从而可以获得非常光滑的流场，没有非物理振荡。与基于高阶有限差分和谱方法的不可压解相比，本文的结果显示了优越性 关于我们 ent流场和统计量，即，总能量、能量耗散、涡度拟能耗散和能谱，其次，考虑了不可压绕流的密度分层问题。在层流区，弱密度分层的解与相应的不可压解符合得很好。然而，在强密度分层，目前的方法给出的解决方案，只有定性的协议。然后，我们介绍了马赫均匀压力修正方法，并在二维圆形凸起通道流中进行了验证。与通常的基于密度的可压缩解相比，从超声速到亚声速的流动范围内都能得到很好的一致性。在准不可压区域，Ma<0.01，通常的可压缩解与本文的解不同。然而，目前的解决方案是几乎相同的不可压缩的解决方案。因此，本文提出的马赫均匀压力修正方法在不可压缩流动的数值模拟中是很有前途的。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