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

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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.