油水渗流动边值问题的迎风差分方法

Upwind Finite Difference Method for Miscible(Oil and Water) Displacement Problem With Moving Boundary Values

可压缩可混溶油、水渗流动边值问题的研究,对重建盆地发育中油气资源运移、聚集的历史和评估油气资源的勘探与开发有重要的价值,其数学模型是一组非线性耦合偏微分方程组的动边值问题.对二维有界域的动边值问题提出一类新的迎风差分格式,应用区域变换、变分形式、能量方法、差分算子乘积交换性理论、高阶差分算子的分解、微分方程先验估计的理论和技巧,得到了最佳误差估计结果.该方法已成功应用到油资评估的数值模拟中.它对这一领域的模型分析,数值方法和软件研制均有重要的价值.

The research of the miscible （oil and water） displacement problem with moving boundary values is of great value to the history of oil-gas transport and accumulation in basin evolution, as well as to the rational evaluation in prospecting and exploiting oil-gas resources. The mathematical model can be described as a coupled system of nonlinear partial differential equations with moving boundary values. For the two-dimensional bounded region, the upwind finite difference schemes were put forward. Some techniques, such as calculus of variations, change of variables, theory of a priori estimates and techniques were adopted. Optimal order estimates are derived for the errors in approximate solutiolts. The research is important both theoretically and practically for model analysis in the field, for model numerical method and for software development.