Conference on Analysis, Modeling and Computation of PDE and Multiphase Flow; Stony Brook, NY

偏微分方程和多相流分析、建模和计算会议；

• 批准号: 0422640
• 负责人: Xiaolin Li
• 金额: $ 1万
• 依托单位: SUNY at Stony Brook
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-08-15 至 2005-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0422640&HistoricalAwards=false
• 关键词: Conference; Analysis; Modeling; Computation; PDE

This award is in partial support to the Conference on Analysis, Modeling and Computation of PDE and Multiphase Flow. It took approximately 250 years from Euler's formulation of the partial differential equations governing the flow of compressible fluids to the proof that such flows with arbitrarily prescribed initial states actually exist. This scientific breakthrough opened a new field in analysis and computation of the problem of multiphase fluid flow. The demonstration that the solutions can exist in weak form which include discontinuous structures poses a great challenge to mathematicians in designing numerical algorithms for the computation of the multiphase flow. The scientific progress in this field has always been an interplay between analysis and computation, by hard work and by mere luck. This conference brings scientists who have made important contribution to the field and those who are striving to find new solutions in more complicated systems and higher dimensions. The speakers will address the proof of existence and uniqueness of the partial differential equations, numerical algorithms to solve such equations and computational examples emerged from scientific and engineering problems which are governed by such partial differential equations. The conference is to foster communication among theoreticians, numerical analysts and computational scientists from universities and national laboratories and between leaders and students in these fields. Theoreticians can predict the qualitative aspects of the solutions while computational scientists will demonstrate the details of the numerical solution which is unknown to the analysts. The PDE and its application to the multiphase flow problem has a large impact in national defense and industry. Such problems are brought from national laboratories to the academic community to seek better mathematical understanding and a better design for numerical algorithms. Many university participants of this conference have connection with national laboratories and industry. Woman scientists play an important role in this research and they are among several plenary and invited speakers of the conference. Others include brilliant graduate students and junior researchers from underrepresented minorities and people with physical disability. The conference also holds a poster session for the graduate students from several universities.

该奖项部分支持PDE和多相流的分析，建模和计算会议。从欧拉提出控制可压缩流体流动的偏微分方程到证明具有任意初始状态的流动确实存在，大约花了250年。这一科学突破为多相流体流动问题的分析和计算开辟了新的领域。证明解可以以弱形式存在，其中包括不连续结构，这对数学家在设计用于多相流计算的数值算法时提出了很大的挑战。这一领域的科学进步一直是分析和计算之间的相互作用，通过努力工作和运气。这次会议带来了对该领域做出重要贡献的科学家，以及那些努力在更复杂的系统和更高维度中找到新解决方案的科学家。演讲者将讨论偏微分方程的存在性和唯一性的证明，解决此类方程的数值算法以及由此类偏微分方程控制的科学和工程问题中出现的计算示例。会议旨在促进来自大学和国家实验室的理论家，数值分析师和计算科学家之间的交流，以及这些领域的领导者和学生之间的交流。理论家可以预测解决方案的定性方面，而计算科学家将展示分析师未知的数值解的细节。偏微分方程及其在多相流问题中的应用在国防和工业领域有着重要的意义。这些问题从国家实验室带到学术界，以寻求更好的数学理解和更好的数值算法设计。这次会议的许多大学参与者与国家实验室和工业界有联系。女科学家在这项研究中发挥了重要作用，她们是会议全体会议和特邀发言人之一。其他人包括来自代表性不足的少数民族和身体残疾人的优秀研究生和初级研究人员。会议还为来自几所大学的研究生举办了海报会议。