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

James Glimm教授和一组美国研究人员将与巴西研究人员在巴西圣保罗天主教大学的Dan Marchesin教授的领导下进行合作研究。研究人员计划追求两个基本的科学目标：了解代表守恒定律的非线性偏微分方程基本解的本质；设计一种算法来构造这些基本解并将其作为具有两个因变量的系统的计算机程序来实现。该程序将用于对提高采收率的流体流动进行高精度模拟。为了优化几种开采方案下的油气采收率，油藏工程师使用计算机模拟来模拟采收率过程。储层流动是用一套控制通过多孔介质流动的偏微分方程来描述的。流体的不同相或组分导致不连续，这些流动的数值模拟通常涉及守恒定律系统的求解。目前还没有一套理论或数值方法来解决这些大规模的所谓黎曼问题，而这正是研究者计划解决的需求。对于许多守恒律系统的黎曼问题的求解和应用，作者做出了重大贡献。在这项联合工作中所开发的理论和计算机程序在气体动力学、燃烧理论、弹性和粘弹性固体、高能物理学和天体物理学——事实上，在任何由非线性守恒定律描述的物理情况中，都有广泛的潜在应用。

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.