Mathematical Sciences: Propagating Fronts By A Consistent Primitive Algorithm With Application To Bubble Dynamics

数学科学：通过一致的原始算法传播前沿并应用于气泡动力学

• 批准号: 9203768
• 负责人: Smadar Karni
• 金额: $ 6万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-08-01 至 1996-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9203768&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Propagating; Fronts; Consistent

The investigator will develop new numerical methods to model weak solutions to nonlinear hyperbolic differential equations derived from a set of conservation laws. Conservation form of the system is widely held as imperative for consistent numerical capturing of shocks. In practice, while this may be true for flows dominated by strong shocks, other flow phenomena may be better modelled by different, not necessarily conservative flow descriptions. In such cases, one may be prepared to sacrifice strict conservation in favor of a nonstrictly conservative model that describes better the dominant flow features. To be reliable, the model should generate acceptably small conservation errors. The investigator shows that propagating fronts is one such phenomenon. Capturing propagating fronts by conservative models gives rise to oscillations and other inaccuracies near material fronts, and is in general unsatisfactory. These are not the common oscillations associated with high order schemes, but rather a result of the simple wave model (i.e. eigenstructure) of the conservative systems. A remedy is to use a nonconservative flow description, which offers a different eigenstructure. It becomes exact near contact surfaces and produces clean oscillation-free interfaces. Near shocks, the model is not exact and conservation errors are committed. A technique recently developed by the investigator offers a cure to this problem. It uses viscous perturbations that render the algorithm conservative to the order of numerical approximation and generate acceptably small conservation errors. The technique has been successfully applied to computing propagating fronts in 1D. The investigator will study several theoretical aspects of this nonstrictly conservative algorithm and its application to the computation of bubble dynamics in several space dimensions. The work of the project involves theoretical analysis and computer simulation of flows. These arise in physical phenomena involving mixing of fluids, the initiation and evolution of vortices, the ignition and evolution of chemical reactions in fluids, and the propagation of flames. The aim of the project is to develop analytical and computational tools to enhance the understanding of the complicated physical phenomena involved. Insight gained this way will supplement experimental data, which are often expensive, difficult or even dangerous to obtain. For example, wind tunnel simulations of space conditions in the upper stratosphere are difficult and expensive to perform and may give unreliable results; studying gun ballistics requires experimenting with strong explosions, which are both expensive and dangerous. Potential impact of this project extends to a variety of industries including the space and aircraft industries (design of space vehicles and of aicraft wings), marine industry (design of boats with improved hydrodynamic properties, the effect of bubbles on submarine hydrodynamics, etc.) and the weapon industries (e.g., internal ballistics of guns).

研究人员将开发新的数值方法 模拟非线性双曲微分方程的弱解 从一组守恒定律导出的方程。养护 系统的形式被广泛认为是一致的必要条件 冲击的数值捕捉。 实际上，虽然这可能是 对于以强冲击为主的流动，其他流动现象 可能会更好地模拟不同的，不一定是保守的 流程描述。在这种情况下，可以准备 牺牲严格的保守性， 更好地描述主导流的保守模型 功能.为了可靠，该模型应生成可接受的 小的保守错误。调查显示， 传播波前就是这样一种现象。捕获传播 保守模型的前沿引起振荡， 材料前沿附近的其他不准确之处， 不满意。这些并不是常见的振荡 高阶格式，而是简单波的结果 保守系统的模型（即特征结构）。补救 是使用非保守流描述，它提供了 不同的特征结构 它在接触面附近变得精确 并产生干净的无振荡界面。近冲击， 模型不精确，并犯下守恒错误。一 研究人员最近开发的技术提供了一种治疗方法， 这个问题它使用粘性扰动， 数值逼近阶守恒算法 并产生可接受的小的守恒误差。该技术 已成功地应用于计算传播前沿， 1D. 研究人员将研究几个理论方面， 这种非严格保守算法及其应用 在几个空间维度中的气泡动力学的计算。 该项目的工作包括理论分析和 流动的计算机模拟。这些都产生于物理现象 包括流体的混合， 涡流，化学反应的点火和演变， 液体和火焰的传播。该项目的目的是 开发分析和计算工具来增强 理解所涉及的复杂物理现象。 通过这种方式获得的见解将补充实验数据， 往往是昂贵的，困难的，甚至是危险的。为 例如，风洞模拟上层空间条件 平流层是困难和昂贵的执行，并可能给予 不可靠的结果;研究枪支弹道学需要 实验强烈的爆炸，这两个都是昂贵的， 也很危险 该项目的潜在影响延伸到 包括航天和航空工业在内的各种工业 （航天器和飞机机翼的设计），海洋工业 （设计具有改进的水动力特性的船只， 气泡对潜艇水动力学的影响等）和 武器工业（例如，枪的内部弹道学）。