Numerical Simulation of Immiscible Flow in Porous Media Based on Combining the Method of Characteristics with Mixed Finite Element Procedures

1988 ◽  
pp. 119-131 ◽  
Author(s):  
Jim Douglas ◽  
Yuan Yirang
Keyword(s):  
Numerical Simulation ◽  
Finite Element ◽  
Porous Media ◽  
Method Of Characteristics ◽  
Mixed Finite Element ◽  
Flow In Porous Media ◽  
Immiscible Flow ◽  
The Method Of Characteristics

scholarly journals Domain Decomposition Modified with Characteristic Mixed Finite Element and Numerical Analysis for Three-Dimensional Slightly Compressible Oil-Water Seepage Displacement

2017 ◽  
Vol 9 (1) ◽  
pp. 143
Author(s):  
Yirang Yuan ◽  
Luo Chang ◽  
Changfeng Li ◽  
Tongjun Sun
Keyword(s):  
Finite Element ◽  
Domain Decomposition ◽  
Method Of Characteristics ◽  
Mixed Finite Element ◽  
Three Dimensional ◽  
Optimal Error Estimate ◽  
Computational Domain ◽  
Time Step ◽  
Slightly Compressible ◽  
The Method Of Characteristics

A parallel algorithm is presented to solve three-dimensional slightly compressible seepage displacement where domain decomposition and characteristics-mixed finite element are combined. Decomposing the computational domain into several subdomains, we define a special function to approximate the derivative at interior boundary explicitly and obtain numerical solutions of the saturation implicitly on subdomains in parallel. The method of characteristics can confirm strong stability at the fronts, and can avoid numerical dispersion and nonphysical oscillation. It can adopt large-time step but can obtain small time truncation error. So a characteristic domain decomposition finite element scheme is put forward to compute the saturation. The flow equation is computed by the method of mixed finite element and numerical accuracy of Darcy velocity is improved one order. For a model problem we apply some techniques such as variation form, domain decomposition, the method of characteristics, the principle of energy, negative norm estimates, induction hypothesis, and the theory of priori estimates of differential equations to derive optimal error estimate in $l^2$ norm. Numerical example is given to testify theoretical analysis and numerical data show that this method is effective in solving actual applications. Then it can solve the well-known 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.

Anisotropic Mesh Adaptivity and Control Volume Finite Element Methods for Numerical Simulation of Multiphase Flow in Porous Media

2015 ◽  
Vol 47 (4) ◽  
pp. 417-440 ◽  
Author(s):  
Peyman Mostaghimi ◽  
James R. Percival ◽  
Dimitrios Pavlidis ◽  
Richard J. Ferrier ◽  
Jefferson L. M. A. Gomes ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Finite Element ◽  
Porous Media ◽  
Finite Element Methods ◽  
Control Volume ◽  
Flow In Porous Media ◽  
Mesh Adaptivity ◽  
Anisotropic Mesh ◽  
And Control ◽  
Control Volume Finite Element
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