Problems in Dynamics of Phase Transitions and Numerical Analysis of Conversation Laws

范海涛 摘要： 该项目的长期目标是了解液相/气相转变的动力学及其数学理论。 液/汽相变是科学和工程中的重要现象。 传统的相变动力学模型与实验结果相比存在一定的差距。 我们建议通过一种不同于传统模型的方法来研究液/汽相变的动力学。该模型是一个具有源项的守恒律系统（系统），基于以下方程： 两相反应流。根据我们的初步研究，这种方法 更适合实验。 为了实现我们的目标， 将追求以下具体的子目标：1）导出系统的定性和定量渐近模型。 2)研究系统中的基本波型及其渐近性等问题 模型，例如，行波，冲击和相位的容许准则 边界和黎曼问题。 3)开发算法对系统进行数值模拟，并开发测试问题以证明此类计算的合理性。 研究与系统数值格式有关的问题 4)研究系统的适定性或其简化渐近性 模型 预计在拟议的支助期结束时，将获得关于该系统定性和定量行为的结果，并将进行数值模拟。将系统的定性和定量行为的结果与实验进行比较。 基于这些比较，可以评估建模的充分性，并且可以进一步改进建模。 预计所获得的结果将有助于理解的液体/蒸汽相变的动力学。 这些现象的数值模拟工具也将从这项工作中产生。 大多数物质有四种相：固相、液相、气相和等离子体相。 相变，例如从水到蒸汽的变化，反之亦然，是日常生活中和我们环境中无处不在的材料的基本现象。许多制造过程，例如半导体制造中使用的单个大晶体的生长，涉及相变。 在飞机穿越云层飞行和水下爆炸过程中，会发生液/汽相变。 液体/蒸汽相变也发生在船只的高速运动部件，例如潜艇的螺旋桨，这消耗能量并使敌人的太阳能设备检测到噪音。 总之，相变不仅是材料的基本科学性质，而且对工业竞争力和国家安全至关重要。 拟议的项目是研究相变的演变，特别是由快速移动的物体或波引起的快速液体/蒸气转变。 目标是建立有效的数学模型，液体/蒸汽转变，同意与实验数据，并开发数值模拟工具，这样的相变。

Haitao Fan Abstract: The long-range goal for the proposed project is to understand the dynamics of liquid/vapor phase transitions and its mathematical theories. Liquid/vapor phase transitions are important phenomena in science and engineering. Traditional models for the dynamics of phase transition, exhibit gaps when compared with experiments. We propose to investigate the dynamics of liquid/vapor phase transitions through an approach different from traditional models. The model is a system of conservation laws with source terms (the system) based on equations for two-phase reactive flows. Based our preliminary studies, this approach promises to better fit experiment. To accomplish our objective, the following specific sub-objectives will be pursued: 1) Derive qualitative and quantitative asymptotic models for the system. 2) Study issues such as basic wave patterns in the system and its asymptotic models, e.g., traveling waves, admissibility criteria for shocks and phase boundaries, and the Riemann problem. 3) Develop algorithms to carry out numerical simulations on the system and develop test problem to justify such computations. Study issues related to numerical schemes for the system 4) Study the well-posedness of the system or its simplified asymptotic models. The expectations are that, at the conclusion of the proposed period of support, results will have been obtained on qualitative and quantitative behavior of the system, and numerical simulations will have been carried out. Results on qualitative and quantitative behavior of the system will be compared with experiments. Based on these comparisons, the adequateness of the modeling can be assessed, and the modeling can be further improved. It is expected that the results obtained will facilitate understanding of the dynamics of liquid/vapor phase transitions. Tools for numerical simulations of such phenomena will also result from this work. Most materials have four phase s: solid, liquid, vapor and plasma phases. Phase transition, such as the change from water to vapor and vice versa, is fundamental phenomena of materials that occur in daily life and everywhere in our environment. Many manufacturing processes, such as the growth of a single large crystal used in semiconductor manufacturing, involve phase transitions. Liquid/vapor phase transitions happen during the flight of airplane through clouds and during underwater explosions. Liquid/vapor phase changes also occur at high speed moving parts of a vessel, such as the propeller of a submarine, which consumes energy and makes noise detectable by enemies' solar devices. In summary, phase transitions are not only fundamental scientific properties of materials but also vital to industrial competitiveness and national security. The proposed project is to study the evolution of phase changes, in particular the rapid liquid/vapor transitions induced by rapid moving body or waves. The objectives are to establish effective mathematical models for liquid/vapor transitions that agree with experimental data, and to develop numerical simulation tools for such phase transitions.