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

本研究主要研究非线性紧致格式在多相流等复杂湍流问题中的应用。紧致格式在湍流模拟中具有分辨率高、相位误差小等优点。然而，对称紧致格式没有任何非线性处理的应用，几乎没有成功的物理间断的流动，由于计划的色散误差。另一方面，ENO型格式有太大的耗散误差，以解决传播的声波。本项目研究了三个试验问题：（1）高马赫数钝体流动对外部声波的感受性，（2）超声速剪切层的声波发射机理，（3）气泡溃灭和微射流。迎风紧致格式的优点是能在较高波数下求解流场，并能在高波数下产生耗散效应，从而抑制数值振荡。对这些格式的进一步处理，如数值通量的凸组合，被证明能成功地捕捉到大的间断和非常小的声波。

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.