NUMERICAL METHOD AND APPLICATION FOR THREEDIMENSIONAL NONLINEAR SYSTEM OF DYNAMICS OF FLUIDS IN POROUS MEDIA

For the system of multilayer dynamics of fluids in porous media, the second order upwind finite difference fractional steps schemes applicable to parallel arithmetic are put forward. Some techniques, such as calculus of variations, energy method, multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates are adopted. Optimal order estimates are derived to determine the error in the second order approximate solution. These methods have already been applied to the numerical simulation of migration-accumulation of oil resources.     

Upwind finite difference method for miscible oil and water displacement problem with moving boundary values

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 the 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 twodimensional bounded region, the upwind finite difference schemes are proposed. Some techniques, such as the calculus of variations, the change of variables, and the theory of a priori estimates, are used. The optimal orderl2-norm estimates are derived for the errors in the approximate solutions. The research is important both theoretically and practically for the model analysis in the field, the model numerical method, and the software development.     

油资源运移聚集并行数值模拟和分析

多层油资源运移聚集并行数值模拟,其功能是重建油气盆地的运移聚集演化史,对于油资源的评价,确度油藏位置,估计油藏贮量均具有重要的价值.从生产实际出发,提出数学模型,构造大规模精细并行计算的耦合算子分裂隐式迭代格式,设计了并行计算程序和并行计算的信息传递和交替方向网格剖分方法.并对不同的网格步长进行了并行计算和分析.对滩海地区进行精细数值模拟,计算结果在油田位置等方面和实际情况相吻合.对模型问题(非线型性耦合问题)进行数值分析,得到最佳阶L²误差估计,解决了这一计算渗流力学和石油地质的困难问题.     

渗流耦合系统动边值问题特征差分方法及其应用

油气运移、聚集史软件的功能是重建盆地发育中油气资源运移、聚集的历史,它对合理评估油气资源的勘探和开发有重要的价值．其数学模型是一组多层对流扩散耦合系统的动边值问题．提出一类特征差分格式,得到最佳阶误差估计结果．对这一领域的模型分析、数值方法和软件研制均有重要的理论和实用价值．     

Numerical Simulation for Evolutionary History of Three-Dimensional Basin

ＮＵＭＥＲＩＣＡＬＳＩＭＵＬＡＴＩＯＮＦＯＲＥＶＯＬＵＴＩＯＮＡＲＹＨＩＳＴＯＲＹＯＦＴＨＲＥＥ－ＤＩＭＥＮＳＩＯＮＡＬＢＡＳＩＮＹｕａｎＹｉ－ｒａｎｇ（袁益让）；ＷａｎｇＷｅｎ－ｑｉａ（王文洽）；ＹａｎｇＤａｎ－ｐｉｎｇ（羊丹平）（Ｄｅｐａｒｔｍｅ...     

非线性多层渗流系统的数值方法及其应用

对多层非线性渗流系统提出适合并行计算的迎风分数步差分格式，利用变分形式、能量方法、差分算子乘积交换性、高阶差分算子的分解、先验估计的理论和技巧，得到收敛性的最佳阶的误差估计．该方法已成功的应用到油资源渗流力学运移聚集数值模拟的生产实际中．     

油水渗流动边值问题的迎风差分方法

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.     

Characteristic finite difference method and application for moving boundary value problem of coupled system

The coupled system of multilayer dynamics of fluids in porous media is to describe the history of oil-gas transport and accumulation in basin evolution.It is of great value in rational evaluation of 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.A kind of characteristic finite difference schemes is put forward,from which optimal order estimates in l^2 norm are derived for the error in the approximate solutions.The research is important both theoretically and practically for the model analysis in the field,the model numerical method and software development.