多孔介质中两相可混溶驱动问题的特征-混合动态有限元方法(英文)

Characteristic-mixed Methods on Dynamic Finite Element Spaces for Two-phase Miscible Flow in Porous Media

数学上,多孔介质中一种不可压流体对另一不可压流体的相溶驱动由两个耦合的非线性偏微分方程组成,其中一个是关于压力的椭圆方程,另一个是关于浓度的抛物方程。本文用特征有限元方法结合动态有限元空间来逼近浓度,而压力和达西速度则由混合元方法来同时逼近。通过采用负模估计,我们给出了收敛性分析与误差估计。

The miscible displacement of one incompressible fluid by another in a porous media is governed by a nonlinear coupled system of two partial differential equations, one of elliptic form for the pressure and the other of parabolic form for the concentration of the fluids. In this paper, the concentration is approximated by a modified method of characteristics （MMOC） combined with dynamic finite element spaces, while the pressure and Darcy velocity of the mixture are approximated simultaneously by a mixed finite element method. By adopting the negative-norm estimate, convergence analysis and error estimates are established.