Development of numerical schemes for the fluid flows with accurate boundary condition

本研究的目的是利用精确的边界条件，建立高精度的流体流动数值格式。对于流体流动的模拟，需要适当地选择数值边界和/或界面。我们考虑了三个数值问题：(A)具有三维自由面或界面的流体流动；(B)与声波相互作用的涡流场的边界条件；(C)与声波相互作用的涡流场的边界条件。(C)高精度、高分辨率格式的边界条件。研究结果如下：(1)在三维不可压缩流动计算中，建立了考虑大密度比、粘度比和表面张力影响的两相流体界面水平集公式。两个上升气泡、浮力液滴与流液界面…相互作用的数值模拟更多的Ce，以及表面波的传播。改进了矢量速度势的边界条件，得到了局域涡量场的精确数值计算方法。利用该方法可以对不同流场中的涡声进行评价，并分析其发声机理。(3)利用无反射边界条件，研究了低雷诺数下流动分离的声学控制。再现了声激励降低翼型分离倾向的现象，并对分离点附近的详细流场进行了分析。(4)在边界附近有集中点的广义网格系统中，发展了高精度、高分辨率的组合紧致格式。与其他有限差分方法相比，该格式给出了更精确的数值结果。较少

The Purpose of this study is to develop high accurate numerical schemes for the fluid flow by using the accurate boundary conditions. For the simulation of the fluid flow, the adequate choice of numerical boundaries and/or interfaces is needed. We considered three numerical problems : (A) the fluid flow with three dimensional free surface or interface, (B) the boundary conditions of the vortical flow field interacting with acoustic waves, and (c) the boundary conditions of the vortical flow field interacting with acoustic waves. and (c) the boundary conditions for the scheme with accuracy and high resolutions. The results of the study are as follows :(1) The level set formulation for the interface of two-phase fluids is developed in the three-dimensional incompressible flow calculations, including large density and viscosity ratio as well as surface tension effects. Numerical simulations carried out for two rising gas bubbles, the interaction of buoyant drops with a fluid-fluid interfa … More ce, and the propagation of surface waves. The results agree with previous experiment data, and make it possible to analyze the physical quantities near the boundaries.(2) Improving the boundary conditions for the vector velocity potential, we get the accurate numerical method for the localized vorticity fields. Using this method, the vortex sounds can be evaluated in the various flow fields, and the sound generation mechanism can be analyzed.(3) Using the no reflective boundary conditions, the acoustic control of flow separation at low Reynolds numbers are studied. We reproduced the phenomena that the tendency toward the separation on an airfoil is reduced by an acoustic excitation, and analyze the detailed flow field near the point of separation.(4) The combined compact scheme with high accuracy and high resolution is developed in the generalized grid system with concentrated points near the boundary. This scheme gives more accurate numerical results compared with the other finite difference methods. Less