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

小行星9706847 本研究系关于两相不可压缩流之Navier-Stokes方程式模拟解之数值技术之分析与发展。 这种方法是专门针对的问题，其特征在于大的密度和粘度跳跃（如空气/水）和刚性，奇异源项，如那些由于表面张力。 这些特征的问题在科学和工业中是极其重要的。 铸造、模具填充、薄膜工艺、挤出、喷射沉积和喷射仅仅是几个例子。 这些问题提出了相当大的挑战。 标准的有限差分方法在密度变化较大的区域附近可能太耗散或太振荡。 由此产生的椭圆方程的执行发散自由条件的速度场（投影步骤）的系数，表现出很大的跳跃在材料界面。 由于表面张力项的发散将作为投影方程的奇异源项出现，因此所得椭圆方程在材料界面处也将具有广泛变化的源项。 在这项研究中，提议者计划与施乐公司的John Andrews博士和Microfab技术公司的大卫华莱士密切合作，开发模拟喷射装置的数值方法。 在喷墨装置中，研究液滴形成的特性是重要的。 由于表面张力在液滴形成过程中起着很大的作用，因此数值方法准确地模拟液滴破碎过程中的表面张力效应是很重要的。 数值方法准确预测喷射液滴的尺寸也很重要。 目前，已经开发了自适应水平集方法和二阶流体体积方法来计算如上所述的两相流动。 拟议的研究目标包括改进的材料边界之间的界面的数值模拟和改进的表面张力的建模，特别是在点的液滴破碎。 在这项研究的过程中，提议者将比较水平集方法的行为与使用非常相似的表面张力公式的流体体积方法的行为。 提议者还将比较数值解与通过渐近方法和施乐公司进行的跌落实验获得的解。 本研究主要探讨不可压缩两相流（如空气和水）数值模拟技术的分析和发展。 两相流问题在科学和工业中是极其重要的。 铸造、模具填充、薄膜工艺、挤出、喷射沉积和喷射仅仅是几个例子。 在这项研究中，提议者计划与施乐公司的John Andrews博士和Microfab技术公司的大卫华莱士密切合作，开发模拟喷射装置的数值方法。 这些公司开发用于喷墨打印机、焊料沉积和微光学元件制造的喷射设备。 在喷射装置中，研究液滴形成特性是重要的。 由于表面张力在液滴形成过程中起着很大的作用，因此数值方法准确地模拟液滴破碎过程中的表面张力效应是很重要的。 数值方法准确预测喷射液滴的尺寸也很重要。 拟议的研究目标包括改进的材料边界之间的界面的数值模拟和改进的表面张力的建模，特别是在点的液滴破裂。 在这项研究的过程中，提议者将比较计算方法的行为与施乐公司进行的跌落实验。

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.