多孔介质中两相不可压混溶驱替的差分流线扩散法及其误差分析  

FDSD METHOD AND ITS ERROR ESTIMATES FOR TWO-PHASE INCOMPRESSIBLE MISCIBLE FLOW IN POROUS MEDIA

作　　者：张强[1] 

机构地区：[1]南开大学数学科学学院,天津300071

出　　处：《应用数学学报》2003年第2期318-327,共10页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(19971050号)资助项目

摘　　要：多孔介质中两相不可压混熔驱替问题可描述为椭圆和抛物耦合的非线性偏微分方程组。对椭圆方程采用混合元方法,而对抛物方程采用差分流线扩散法,本文构造了求解该问题的差分流线扩散-混合元格式。最后,给出所构造格式按L~∞(L^2)模的拟最优误差阶估计。The miscible displacement of one incompressible fluid by another in a porous medium is modeled by a nonlinear system of two partial differential equations. The pressure equation is elliptic, while the concentration is parabolic but normally convection-dominated. In this paper, a finite-different streamline diffusion with mixed finite element method is defined, and the quasi-optimal convergence rates in the norm L(L2) is derived.

关 键 词：多孔介质 两相不可压混溶驱替 差分流线扩散法 误差分析 非线性偏微分方程 压力方程 饱和度方程 混合元方法 差分流线扩散-混合元格式 

分 类 号：O357.3[理学—流体力学] O241.82[理学—力学]