APPLICATION OF NON-LINEAR COMPACT SCHEMES TO COMPLEX TURBULENCE DIRECT NUMERICAL SIMULATIONS SUCH AS MULTI-PHASE FLOW

在本研究项目中，研究了非线性紧凑格式在具有不连续面的复杂湍流模拟中的应用，如多相流湍流。紧凑格式在湍流模拟中具有分辨率高、相位误差小等优点。然而，不作非线性处理的对称紧凑格式由于存在色散误差而难以成功地应用于具有物理不连续的流动。另一方面，eno型方案的耗散误差太大，无法分辨传播的声波。本课题研究了三个测试问题；(1)高马赫数钝体流对外部声波的接受性；(2)超声速剪切层声波发射机理；(3)气泡崩塌与微射流。逆风紧致格式在高波数范围内具有解决流场的优势，并且在高波数范围内对数值振荡具有耗散效应，这些格式的高级处理，如数值通量的凸组合，被证明可以成功捕获大的不连续和很小的声波。对于气泡畸变和击穿模拟，采用了非线性滤波技术。

In this research project, application of non-linear compact schemes to simulations of complex turbulence with discontinuities, such as multi-phase flow turbulence, is studied. Compact schemes have a few advantages of high-resolution and minimum phase-error for turbulence simulations. However, application of symmetric compact schemes without any nonlinear treatment to the flow with physical discontinuities has hardly been successful due to the schemes dispersion error. On the other hand, ENO-type schemes have too large dissipation error to resolve propagating acoustic waves. In this project, three test problems have been investigated; (1) High Mach number blunt body flow receptivity to external acoustic waves, (2) Acoustic wave emission mechanism from supersonic shear layer, (3) Bubble collapse and microjet. Upwind compact schemes have an advantage to resolve the flow fields up to rather high-wavenumber and present a dissipation effect to damp numerical oscillation at only high-wavenumbers Advanced treatments of these schemes, such as convex combination of numerical flux, were proved to be successful to capture both large discontinuities and very small acoustic waves, For bubble distortion and breakdown simulations, a non-linear filter technique was employed.