袁益让^*

（  山东大学数学研究所；  ）

摘要： 对多层非线性渗流方程的耦合系统提出适合并行计算的二阶和一阶特征分数步差分格式.利用变分形式,能量方法,二维和三维网格配套,双二次(一次)插值,差分算子乘积交换性,高阶差分算子分解,先验估计的理论和技巧,对二阶格式得到收敛性的最佳阶的L2误差估计.对一阶格式亦得到收敛性的L2误差估计.该方法已成功应用到多层油资源运移聚集的数值模拟生产实际中.
关键词： 非线性耦合系统, 特征差分, 分数步, 二阶和一阶, 收敛性

Yuan Yirang ^*

（  Institute of Mathematics, Shandong University；  ）

Abstract： For nonlinear coupled system of multilayer fluid dynamics in porous media, the second order and first order characteristic finite difference fractional steps method applicable to parallel arithmetic is put forward, and two-dimensional and three-dimensional schemes are used to form a complete set. Some techniques, such as calculus of variations, energy method, piecewise biquadratic interpolation, multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates are adopted. Optimal order estimates in L2 norm are derived to determine the error in the second order approximate solution. This method has already been applied to the numerical simulation of multilayer fluid dynamics in porous media.

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