Efficient, High Resolution, Numerical Methods for Free-boundry Problems with Surface Tension

9706847萨斯曼这项研究涉及两相不可压缩流动的N-S方程的数值模拟技术的分析和发展。这种方法专门针对密度和粘度跳跃较大(例如空气/水)和僵硬、单一源项的问题，如表面张力引起的问题。这些特性的问题在科学和工业中极其重要。铸造、充模、薄膜加工、挤压、喷射沉积和喷射只是其中的几个例子。这些问题带来了相当大的挑战。在密度变化较大的区域附近，标准的有限差分方法要么耗散太大，要么太振荡。在速度场上实施无散度条件(投影步长)所得到的椭圆型方程的系数在材料界面处表现出很大的跳跃。由于表面张力项的发散将表现为投影方程的奇异源项，因此所得到的椭圆型方程在材料界面处也将具有变化很大的源项。在这项研究中，提出者计划与施乐的约翰·安德鲁斯博士和Microfab Technologies的大卫·华莱士密切合作，开发建立喷射设备模型的数值方法。在喷墨装置中，研究液滴的形成特性是非常重要的。由于表面张力在液滴形成过程中起着很大的作用，因此准确地模拟液滴破碎过程中的表面张力效应对于数值方法来说是很重要的。对于数值方法来说，准确预测排放液滴的大小也是很重要的。目前，已发展了一种自适应水平集方法和二阶流体体积方法来计算上述两相流动。拟议研究的目标包括改进材料边界之间界面的数值模拟和改进表面张力的模拟，特别是在液滴破碎点。在这项研究的过程中，提出者将比较Level Set方法和流体体积方法的行为，后者使用非常相似的表面张力公式。提出者还将把数值解与通过渐近方法和施乐进行的Drop实验获得的解进行比较。这项研究是关于不可压缩两相流(如空气和水)数值模拟技术的分析和发展。两相流中的问题在科学和工业中都是极其重要的。铸造、充模、薄膜加工、挤压、喷射沉积和喷射只是其中的几个例子。在这项研究中，提出者计划与施乐的约翰·安德鲁斯博士和Microfab Technologies的大卫·华莱士密切合作，开发建立喷射设备模型的数值方法。这些公司开发用于喷墨打印机、焊料沉积和微型光学元件制造的喷射设备。在喷射装置中，研究液滴的形成特性是非常重要的。由于表面张力在液滴形成过程中起着很大的作用，因此准确地模拟液滴破碎过程中的表面张力效应对于数值方法来说是很重要的。对于数值方法来说，准确预测排放液滴的大小也是很重要的。拟议研究的目标包括改进材料边界之间界面的数值模拟和改进表面张力的模拟，特别是在液滴破碎点。在这项研究的过程中，提出者将把计算方法的行为与施乐进行的水滴实验进行比较。

9706847 Sussman This research concerns the analysis and development of numerical techniques for modeling solutions of the Navier-Stokes equations for two-phase incompressible flow. This methodology is specifically targeted at problems characterized by large density and viscosity jumps (e.g. air/water) and stiff, singular source terms, such as those due to the surface tension force. Problems with these features are extremely important in science and industry. Casting, mold filling, thin film processes, extrusion, spray deposition and jets are just a few examples. These problems present considerable challenges. Standard finite difference methods can either be too dissipative or too oscillatory near regions of large density variations. The resulting elliptic equation for enforcing the divergence free condition on the velocity field (projection step) has coefficients that exhibit a large jump at material interfaces. The resulting elliptic equation will also have a widely varying source term at material interfaces, since the divergence of the surface tension term will appear as a singular source term for the projection equation. In this research, the proposers plan to work in close collaboration with Dr. John Andrews of Xerox and David Wallace of Microfab technologies in developing numerical methods for modeling jetting devices. In an ink-jet device, it is important to study the characteristics of droplet formation. Because surface tension plays a large role in the droplet formation process, it is important for a numerical method to accurately model the surface tension effects during break-up of a droplet. It is also important for a numerical method to accurately predict the size of emitted droplets. Currently an adaptive level set method and a second order volume-of-fluid method have been developed for computing two-phase flows as characterized above. Objectives of the proposed research include improved numerical modeling of the interface between material boundaries and improved mo deling of surface tension, especially at points of droplet break-up. In the process of this study, the proposers will compare the behavior of the levelset method to that of the volume of fluid method which use a very similar formulation for the surface tension force. The proposers will also compare numerical solutions to solutions obtained via asymptotic methods and drop experiments conducted by Xerox. This research concerns the analysis and development of numerical techniques for modeling incompressible two-phase flow (such as air and water). Problems in two-phase flow are extremely important in science and industry. Casting, mold filling, thin film processes, extrusion, spray deposition and jets are just a few examples. In this research, the proposers plan to work in close collaboration with Dr. John Andrews of Xerox and David Wallace of Microfab technologies in developing numerical methods for modeling jetting devices. These companies develop jetting devices used in ink-jet printers, solder deposition and the fabrication of micro-optical elements. In a jetting device, it is important to study the characteristics of droplet formation. Because surface tension plays a large role in the droplet formation process, it is important for a numerical method to accurately model the surface tension effects during break-up of a droplet. It is also important for a numerical method to accurately predict the size of emitted droplets. Objectives of the proposed research include improved numerical modeling of the interface between material boundaries and improved modeling of surface tension, especially at points of droplet break-up. In the process of this study, the proposers will compare the behavior of the computational method with drop experiments conducted by Xerox.