二维可压缩油水两相渗流动边值问题的特征差分方法

可压缩可混溶油、水两相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偶合偏微分方程组的动边值问题．本文对二维有界域的两类边值问题提出一类新的特征差分格式，应用区域变换、时间的变步长、粗细网格配套、变分形式、先验估计的理论和技巧，得到了最佳阶l2误差估计结果．将J．Douglas，Jr．提出的著名方法，成功地拓广到这一新领域，并得到实质性进展．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 CHARACTERISTIC FINITE DIFFERENCE METHOD FOR 2-DIMENSIONAL COMPRESSIBLE TWO-PHASE (OIL AND WATER) DISPLACEMENT PROBLEM WITH MOVING BOUNDARY VALUE

The research of the compressible miscible two-phase (oil and water) displacement problem with moving boundary value 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 resoures. The mathematical model can be described as a coupled system of nonlinear partial differential equations with moving boundary value. For a generic case of two-dimensional bounded region with two classes of boundary value problems, we put forward a kind of characteristic finite difference schemes and make use of thick and thin grids to form a complete set, the calculus of variations, the change of variables and of the theory of prior estimates and techniques. Optimal order estimates in l2 norm are derived for the errors in approximate solutions. The research is important both theoretically and practically for model analysis in the field, for model numerical method and for solfware development.