U.S.-Brazil Cooperative Research on Fundamental Solutions ofthe Nonlinear Conservation Laws of Oil Reservoir Simulation (Applied Mathematics)

美巴油藏模拟非线性守恒定律基本解合作研究（应用数学）

• 批准号: 8612605
• 负责人: James Glimm
• 金额: $ 2.4万
• 依托单位: New York University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-07-15 至 1989-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8612605&HistoricalAwards=false
• 关键词: U.S.; Brazil; Cooperative; Research; Fundamental

Professor James Glimm and a group of U.S. researchers will conduct cooperative research with a group of Brazilian researchers under the leadership of Professor Dan Marchesin of the Pontificia Universidade Catolica of Rio de Janeiro. The investigators plan to pursue two basic scientific goals: to understand the nature of the fundamental solutions for the nonlinear partial differential equations representing conservation laws; and to devise an algorithm for the construction of these fundamental solutions and implement it as a computer program for systems with two dependent variables. This program will be used to perform highly accurate simulations of fluid flow in enhanced oil recovery. To optimize the recovery of hydrocarbons under several exploitation schemes, oil reservoir engineers use computer simulation to model the recovery process. The reservoir flow is described by a system of partial differential equations governing flow through a porous medium. Different phases or components of the fluid lead to discontinuities and numerical simulation of these flows often involves the solution of a system of conservation laws. At present there does not exist a body of theory or of numerical methods for solutions of these so-called Riemann problems in the large, and it is this need that the investigators plan to address. The collaborators have made substantial contributions to solving the Riemann problem for many systems of conservation laws and utilizing the solutions in applications. The theory and the computer programs to be developed in this joint work have broad potential application to gas dynamics, to combustion theory, to elastic and visco-elastic solids, and to high energy physics and astrophysics -- in fact, to any physical situation described by nonlinear conservation laws.

詹姆斯·格里姆教授和一组美国研究人员将进行 与一组巴西研究人员合作研究， 宗座大学教授Dan Marchesin的领导 里约热内卢的Catolica。 调查人员计划追查两个基本问题 科学目标：了解基本的 非线性偏微分方程的解， 守恒定律;并设计一种算法， 这些基本的解决方案，并将其实现为计算机程序， 两个因变量的系统 该计划将用于 在强化油中进行流体流动的高精度模拟 复苏 多种开采方式下油气采收率的优化 计划，油藏工程师使用计算机模拟， 恢复过程。 储层流动由以下系统描述： 通过多孔介质的偏微分方程。 流体的不同相或组分导致不连续性， 这些流动的数值模拟通常涉及到一个 守恒定律体系。 目前还没有一个机构， 理论或数值方法的解决方案，这些所谓的黎曼 大的问题，正是这种需要，调查人员计划 来解决。 合作者做出了巨大贡献， 解决许多守恒律系统的黎曼问题， 在应用中使用解决方案。 理论和计算机 在这项联合工作中开发的方案具有广泛的潜力 应用于气体动力学，燃烧理论，弹性和 粘弹性固体，以及高能物理和天体物理学-在 事实上，对于任何由非线性守恒描述的物理情况， 法律为