可压多孔介质流的扩展混合元解法  

Expanded mixed finite element method for compressible miscible displacement in heterogeneous porous media

作　　者：于金彪[1] 任永强[2,3] 曹伟东[1] 鲁统超[2] 程爱杰[2] 戴涛[1] 

机构地区：[1]中国石化股份胜利油田分公司勘探开发研究院,山东东营257015 [2]山东大学数学学院,山东济南250100 [3]齐鲁工业大学理学院,山东济南250353

出　　处：《山东大学学报（理学版）》2017年第8期25-34,共10页Journal of Shandong University(Natural Science)

基　　金：国家科技重大专项资助基金(2011ZX05011-004;2011ZX05052)

摘　　要：讨论多孔介质中两种可压缩流体混溶驱动问题数值方法,假定介质是各向异性的,渗透率系数为张量形式。压力方程采用扩展混合元方法求解压力变量、梯度变量,以及速度变量;浓度方程采用标准有限元方法求解,这一方法对各向异性渗透率多孔介质流可以获得更可靠的数值解。构造了半离散数值格式,通过理论分析得到了压力、速度以及浓度等变量的最优L^2模误差估计,对浓度变量获得了H^1模最优误差估计。We consider the numerical methods for the mathematical model describing the transport and diffusion process of porous media flow. There are two kinds of fluids, one is displaced by another, which are compressible and miscible. The media is supposed to be heterogeneous, so the permeability is of full tensor form. For the pressure equation, an expanded mixed finite dement method is introduced to solve the variables of pressure, gradient, and velocity. For the concentration equation, a Galerkin finite dement formulation is constructed to solve the variable of concentration. This approach aims at obtaining more reliable numerical solutions for porous media flow with heterogenous permeability. By means of theoretical analysis, optimal error estimates in L2-norm for pressure and in H1-norm for concentration are derived.

关 键 词：扩展混合元 多孔介质 渗透率张量 可压缩 混溶驱动问题 误差估计 

分 类 号：O241.82[理学—计算数学]