TIME STEPPING ALONG CHARACTERISTICS FOR THE FINITE ELEMENT APPROXIMATION OF COMPRESSIBLE MISCIBLE DISPLACEMENT IN POROUS MEDIA
多孔介质中可压缩可混溶驱动问题的特征—有限元方法

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.