三维多组分可压缩驱动问题的分数步特征差分方法  

CHARACTERISTIC FINITE DIFFERENCE FRANCTIONAL STEPS METHODS FOR THREE-DIMENSIONAL COMPRESSIBLE MULTICOMPONENT DISPLACEMENT PROBLEM

作　　者：袁益让[1] 

机构地区：[1]山东大学数学研究所,济南250100

出　　处：《应用数学学报》2001年第2期242-249,共8页Acta Mathematicae Applicatae Sinica

基　　金：国家重点基础研究项目;国家攀登计划项目;国家攻关项目;国家教育部博士点基金资助项目.

摘　　要：本文提出三维多组分驱动问题的分数步长特征差分格式，并应用变分形式、能量方法、粗细网格配套、叁二次插值、高阶差分算子的分解和乘积交换性理论和技巧，得到最佳阶 Ｌ~２误差估计．该方法已成功应用到油资源评估、强化采油数值模拟和海水入侵预测和防治的数值模拟中．For three-dimensional compressible multicomponent displacement problem a kind of characteristic finite difference franctional steps methods is put forward thick and thin grids are used to form a complete some techniques, such as piecewise product threefoldquadratic interpolation, of calculus of variations, multiplicative commutation rule of difference operators, decomposition of high order difference operators, the prior estimates and techniques are adopted. Optimal order estimates in L^2 norm are derived to determine the error in the approximate solution.

关 键 词：多组分驱动 三维可压缩 分数步特征差分 L^2估计 数模应用 非线性偏微分方程组 初边值问题 

分 类 号：TE357.4[石油与天然气工程—油气田开发工程] O175.8[理学—数学]