多孔介质中可压缩驱动问题的全离散分裂正定混合元方法

A fully-discrete splitting positive definite mixed element scheme finite for compressible miscible displacement in porous media

提出了数值模拟多孔介质中可压缩驱动问题的全离散分裂正定混合元方法.引入分裂正定混合有限元方法来求解抛物型的压力方程.混合有限元方程组是对称正定的,并且流函数方程不依赖于压力方程.采用标准的Garlerkin方法来处理对流-扩散型的饱和度方程.给出了此方法的全离散格式,并分析了该全离散格式的收敛性.

A miscible displacement of one compressible fluid by another in a porous medium is governed by a nonlinear parabolic system. A new mixed finite element method, in which the mixed element system is symmetric positive definite and the flux equation is separated from pressure equation, is introduced to solve the pressure equation of parabolic type, and a standard Galerkin method is used to treat the convection-diffusion equation of concentration of one of the fluids. A fnlly-discrete scheme is given and the convergence of the scheme is analyzed.