多孔介质中可压缩可混溶驱动问题的特征—有限元方法

在有界区域上多孔介质中可压缩可混溶的油、水两相驱动问题是由非线性偏微分方程组的初、边值问题所决定.Douglas和Roberts曾提出其数学模型并研究了半离散化方法.本文对压力方程采用有限元和混合元两种方法.对饱和度方程采用特征—有限元方法.此方法的截断误差较标准有限元小的多,随之饱和度的计算更加精确.且可用

TIME STEPPING ALONG CHARACTERISTICS FOR THE FINITE ELEMENT APPROXIMATION OF COMPRESSIBLE MISCIBLE DISPLACEMENT IN POROUS MEDIA

Miscible displacement of one compressible fluid by another in a porous medium is mo-deled by a nonlinear coupled system of two partial differential equations. Two finite elementprocedures are introduced to approximate the concentration of one of the fluids and the pres-sure of the mixture. The concentration is treated by a combination of a Galerkin method andthe method of characteristics in both procedures, while the pressure is treated hy either a Ga-lerkin method or by a parabolic mixed fini~+e element method. Optimal convergence rates in H'are demonstrated for these schemes. Time stepping along the characteristics of the hyperbolicpart of the concentration equation is shown to result in smaller time-truncation errors thanthose of standard methods, Numercal results published elsewhere have confirmed that largertime steps are appropriate with these schemes, and that the approximaxions exhibit improvedqualitative behavior.