拉伸流中有表面活性剂的液滴运动的数值模拟-计算数学专业论文.docxVIP

I I 摘 要 在这篇论文中，我们研究的是有表面活性剂的液滴在拉伸流的数值模拟。我们 在文章中运用了一种解决这种问题的数值方法-水平集连续表面力方法。 水平集连续表面力方法的提出是用来解决含不相溶表面活性剂的二相流的问 题。我们的方法重算了Navier–Stokes 方程对含一个液滴的不相溶表面活性剂的伸 张流。在level-set方法和离散的Dirac函数中要用到界面运输和界面跳转条件。在密 度加权投影方法的基础上，采用了一个稳定的半隐式方案，即以分离速度分量解决 正规化的Navier–Stokes方程。LS-CSF方法在二维中的运算很好，它能够计算广泛 的粘度比和密度比率的流体。 现在水平集方法很好的解决了图像的拓扑结构，得到了广泛的应用。例如说Caselles等 人运用水平集方法来实现了图像切割；在[1]中就给出了Chan-Vese在图像分割中的 应用模型和结论;而有些学者则把水平集方法运用到医学中。还有一些学者，则把水 平集方法应用在图像去噪中. 最后在数值模拟中，模拟了一个液滴中的变形情况，两个液滴交互的模拟显 示,表面活性剂可以发挥重要作用,可以防止液滴聚结。在三维中的多点表面活性剂 液滴交互作用的模拟已被证明。 关键词：水平集方法，拉伸流，不相溶表面活性剂，表面张力，连续表面力。 I II Abstract In this thesis, Our study the numerical simulation of surfactant droplet motion in extension flow.This we introduce a numerical method for a solution to this problem - the level set method of continuous surface force. Level set continuous surface force method proposed is used to solve the two- phase flow problems with insoluble surfactant.Interfacial transport and interfacial jump conditions are treated using the level-set method and the discrete Dirac func- tion. Based on the density weighted projection method, use a stable semi-implicit scheme to solve the regularization of the Navier-Stokes equations.LS-CSF method for computing is well in two-dimensional , it can be calculated that a wide range of fluid viscosity ratio and density ratio. This is a good solution to the topology of the image to obtain a wide range of applications. Such as Caselles use level set method to achieve image cutting;Chan- Vese image segmentation model and conclusions are given in the literature [1];Some scholars put the level set method applied to medicine,For example, the electronic map shape jump and image restoration.Some scholars put the level set method is used in image deionising. Finally,in the numerical simulation to simulate the deformation of a droplet.Simulations on two drop interaction shows that surfactant can play a critical role in preventing drop coalescence.In the 3D multi-point surfactant droplet interaction sim