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

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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