scholarly journals A Numerical Method for Compressible Model of Contamination from Nuclear Waste in Porous Media

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Zhifeng Wang
Keyword(s):  
Porous Media ◽  
Method Of Characteristics ◽  
Mixed Finite Element ◽  
Grid Method ◽  
Thermal Conditions ◽  
Mixed Finite Element Method ◽  
Fine Grid ◽  
Modified Method ◽  
Optimal Accuracy ◽  
Modified Method Of Characteristics

This paper studies and analyzes a model describing the flow of contaminated brines through the porous media under severe thermal conditions caused by the radioactive contaminants. The problem is approximated based on combining the mixed finite element method with the modified method of characteristics. In order to solve the resulting algebraic nonlinear equations efficiently, a two-grid method is presented and discussed in this paper. This approach includes a small nonlinear system on a coarse grid with size H and a linear system on a fine grid with size h . It follows from error estimates that asymptotically optimal accuracy can be obtained as long as the mesh sizes satisfy H = O h 1 / 3 .

scholarly journals Modified Method of Characteristics Combined with Finite Volume Element Methods for Incompressible Miscible Displacement Problems in Porous Media

2014 ◽  
Vol 2014 ◽  
pp. 1-16
Author(s):  
Sarvesh Kumar ◽  
Sangita Yadav
Keyword(s):  
Porous Media ◽  
Finite Volume ◽  
Method Of Characteristics ◽  
Miscible Displacement ◽  
Volume Element ◽  
Modified Method ◽  
Finite Volume Element ◽  
Velocity Equation ◽  
Modified Method Of Characteristics ◽  
Concentration Equation

The incompressible miscible displacement problem in porous media is modeled by a coupled system of two nonlinear partial differential equations, the pressure-velocity equation and the concentration equation. In this paper, we present a mixed finite volume element method (FVEM) for the approximation of the pressure-velocity equation. Since modified method of characteristics (MMOC) minimizes the grid orientation effect, for the approximation of the concentration equation, we apply a standard FVEM combined with MMOC. A priori error estimates in L∞(L2) norm are derived for velocity, pressure and concentration. Numerical results are presented to substantiate the validity of the theoretical results.

An Efficient Two-Grid Scheme for the Cahn-Hilliard Equation

2014 ◽  
Vol 17 (1) ◽  
pp. 127-145 ◽  
Author(s):  
Jie Zhou ◽  
Long Chen ◽  
Yunqing Huang ◽  
Wansheng Wang
Keyword(s):  
Mixed Finite Element ◽  
Three Dimensional ◽  
Grid Method ◽  
Mixed Finite Element Method ◽  
Fine Grid ◽  
Poisson Equations ◽  
Hilliard Equation ◽  
Grid Scheme ◽  
Speed Up ◽  
Cahn Hilliard Equation

AbstractA two-grid method for solving the Cahn-Hilliard equation is proposed in this paper. This two-grid method consists of two steps. First, solve the Cahn-Hilliard equation with an implicit mixed finite element method on a coarse grid. Second, solve two Poisson equations using multigrid methods on a fine grid. This two-grid method can also be combined with local mesh refinement to further improve the efficiency. Numerical results including two and three dimensional cases with linear or quadratic elements show that this two-grid method can speed up the existing mixed finite method while keeping the same convergence rate.

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