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对多层渗流方程组合系统提出适合并行计算的二阶和一阶两类迎风分数步长差分格式 ,利用变分形式、能量方法、二维和三维格式的配套、隐显格式的相互结合、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 ,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 .该方法已成功地应用到多层油资源运移聚集的评估生产实际中 ,得到了很好的数值模拟结果 .
Two kinds of second order and first order windward fractional step difference schemes suitable for parallel computing are proposed for multi-layer seepage equation system. By using variational form, energy method, two-dimensional and three-dimensional format, hidden and explicit format, The L2 order error estimate of the best order of the convergence for the second order format is also obtained for the L2 order error of the first order form as well as the L2 error estimate for the first order form The method has been successfully applied to the evaluation and production of multi - layer oil migration and accumulation, and good numerical results have been obtained.