A stochastic mixed finite element heterogeneous multiscale method for flow in porous media

2011 ◽  
Vol 230 (12) ◽  
pp. 4696-4722 ◽  
Author(s):  
Xiang Ma ◽  
Nicholas Zabaras
Keyword(s):  
Finite Element ◽  
Porous Media ◽  
Mixed Finite Element ◽  
Multiscale Method ◽  
Flow In Porous Media ◽  
Heterogeneous Multiscale

scholarly journals New Scheme of Finite Difference Heterogeneous Multiscale Method to Solve Saturated Flow in Porous Media

2014 ◽  
Vol 2014 ◽  
pp. 1-19
Author(s):  
Fulai Chen ◽  
Li Ren
Keyword(s):  
Porous Media ◽  
Finite Difference ◽  
Sudden Change ◽  
Multiscale Method ◽  
Flow In Porous Media ◽  
Computational Time ◽  
Saturated Water ◽  
Comparable Accuracy ◽  
Multiscale Finite Element ◽  
Heterogeneous Multiscale

A new finite difference scheme, the development of the finite difference heterogeneous multiscale method (FDHMM), is constructed for simulating saturated water flow in random porous media. In the discretization framework of FDHMM, we follow some ideas from the multiscale finite element method and construct basic microscopic elliptic models. Tests on a variety of numerical experiments show that, in the case that only about a half of the information of the whole microstructure is used, the constructed scheme gives better accuracy at a much lower computational time than FDHMM for the problem of aquifer response to sudden change in reservoir level and gives comparable accuracy at a much lower computational time than FDHMM for the weak drawdown problem.

Numerical Analysis for Two-phase Flow in Porous Media

2003 ◽  
Vol 3 (1) ◽  
pp. 59-75
Author(s):  
Zhangxin Chen
Keyword(s):  
Finite Element ◽  
Porous Media ◽  
Error Estimates ◽  
Finite Element Methods ◽  
Compressible Flows ◽  
Mixed Finite Element ◽  
Flow In Porous Media ◽  
Optimal Order ◽  
Two Phase ◽  
Characteristic Finite Element

Abstract In this paper we derive error estimates for finite element approximations for partial differential systems which describe two-phase immiscible flows in porous media. These approximations are based on mixed finite element methods for pressure and velocity and characteristic finite element methods for saturation. Both incompressible and compressible flows are considered. Error estimates of optimal order are obtained.

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