【作者】 刘海朋；

【导师】 张宏伟；

【作者基本信息】 大连理工大学 ， 运筹学与控制论， 2010， 硕士

【摘要】 自由表面流动问题普遍存在于化工、冶金、航空航天、材料科学等领域中,其过程中自由表面的位置随着液体的运动而变化,而且自由界面的运动对系统的行为具有重要的影响,其已成为流体动力学领域非常关注的问题。本文研究的主要课题是研究自由运动界面的变化情况和与其相关的不可压缩粘性流动的Navier-Stokes方程组的解法,对自由界面的流动采用VOF (volume of fluid)来跟踪自由界面的运动变化情况,其基本思想是在整个流场中定义一个满足对流方程的流体体积函数,空单元时值为0；满单元时值为1；单元为界面单元时值介于0到1之间。讨论了自由界面重构的的四种主要的方法,H-N法、积分平均型TVD格式,FCT法和’Youngs方法,通过四种方法的比较,详细说明了四种方法在处理自由表面流动问题时在精度,效率方面的好坏。并且给出了四种方法在平移场和剪切场中的数值模拟结果。通过理论分析,本文推导出了二维不可压缩粘性流动的Navier-Stokes方程组,介绍了四种主要的求解N-S方程组的数值解法,包括投影法、人工压缩性方法、压力泊松方程法和压力修正算法。介绍了交错网格在处理速度与压力耦合过程的具体应用,有效地解决了速度和压力存在于同一套网格中出现的棋盘式不合理压力场的问题。并且给出了在交错网格下N-S方程组的具体离散形式和相应的边界条件的处理方法,推导出了在交错网格下的压力修正方程的具体表达形式。在求解可压缩粘性流动的Navier-Stokes方程组时时间项采用向前差分,对流项-扩散项采用中心差分格式。为了加快速度和压力的收敛,在具体的求解过程中对相应的压力和速度的修正采取亚松弛技术。在最后,为了验证压力修正算法的有效性,给出了二维驱动方腔流动的数值模拟结果。更多还原

【Abstract】 The free surface flow problems are commonly found out in the fields of chemical, metallurgy, aviation and aerospace and material science. In this process, the position of the free surface changes along with the movement of liquid, moreover, the movement of the free surface has a great influence on the system.it has become a great concern in the field of fluid dynamics.The task of this paper is to study the movement of the free surface associated flow of an incompressible viscous Navier-Stokes equations solution. For the free interface flow volume,we use the VOF (volume of fluid) to track the free interface motion changes,the basic idea of which is that a volume fluid function which satisfies convection function, is defined in whole flow flied. When the cell is empty, the function equals 0; when the cell is full, the function equals 1; when the cell contains interface, the function between 0 and 1. We compare with four kinds of methods to solve VOF function:Hirt & Nichols method, Integral mean type TVD scheme, FCT method and Youngs method. By comparison of four methods, detailed description of the four methods in dealing with free surface flow problems in accuracy, efficiency, good or bad. And gives numerical simulation resultsOf four ways to cut farm field and translation field.Through theoretical analysis,this paper deduceds two-dimensional incompressible vis-cous flow navier-stokes equations, and introduces four major numerical solution, including projection method, artificial compressibility method, pressure poisson equation method and pressure correction algorithm, solving the navier-stokes equations. Staggered grid in-troduced in the processing speed and pressure coupling process of the specific application, can effectively solve the speed and pressure on the same appear in a grid Chessboard prob-lem of unreasonable pressure field.Besides, we give the discrete form of the navier-stokes equations and the form of pressure correction equation in the staggered grid. Using time difference forwards and convection-dispersion central difference format. To speed up the convergence velocity and pressure, in particular the process of solving the corresponding amendments to the pressure and velocity relaxation techniques. In the last, we give an example of a driver of party cavity flow simulation results to verify the effectiveness of the algorithm.更多还原