Numerical Simulation of a Rigid Ball in Air Falling into Water Using a Joint Method of Level Set and Immersed Boundary

• Main Authors: Tsung-po Chen, 陳棕柏
• Other Authors: Ching-Biao Liao
• Format: Others
• Language: zh-TW
• Published: 2008
• Online Access: http://ndltd.ncl.edu.tw/handle/45038461965750140900

碩士 === 逢甲大學 === 水利工程與資源保育研究所 === 96 === Fluid-structure interaction problems have been a challenging subject for computational fluid dynamics, not to mention if the problem involves a free surface between two fluids such as water and air. While level set methods have been celebrating huge success than ever in simulating two-phase flows, various novel and efficient immerse boundary methods have been recently applied successfully to solve difficult fluid-structure interaction problems. However, few methods were reported to solve the fluid-structure interaction problems involving free surface, which can be seen as a kind of three-phase flow problems. Those methods are difficult to implement, which motivated us to develop an efficient joint method of level set and immerse boundary for it. Here incompressible Navier-Stokes equations together with the level set equation are discretized by finite difference method in simple staggered Cartesian grids, with the accuracy of order in space is 2nd order, featuring central difference for the viscous, pressure, and surface tension terms and 2nd-order upwind scheme for convection term. Projection method is employed here with pressure Poisson equation to replace divergence-free condition. 2nd-order Adams-Bashforth method is used for the time-integration of convective, viscous, surface tension and body force terms, and forward Euler method for pressure correction and virtual force terms. The overall accuracy in space and time so far is 2nd order. Since the level set function requests extra accuracy, a 5th-order WENO scheme incorporated with 3rd order Runge-Kutta method for time integration is used to solve the level set equation to track the interface of two fluids (the zero level set). As to the solid part, an immerse boundary method with direct forcing is applied to simulate a solid object moving in two fluids. Volume of solid interpolation is employed to obtain further accuracy in space for flow near the solid without losing the easiness to compute the force exerted on solid. In this study, we used Cate(2002) experiment of a ball falling in silicone oil used to verify the numerical model. The falling velocity and moving trajectory of ball compared with the previous research is very agreement. Two fluid-structure interaction problems with free surface are simulated. They are (i) solid ball falls freely from the air into liquid ; (ii) the high speed ball falls into liquid from the air. We found that the numerical model is quite successful.