Solutions of one-dimensional water flow and mass transport equations in variably saturated porous media by the finite element method

1990 ◽  
Vol 119 (1-4) ◽  
pp. 151-167 ◽  
Author(s):  
Vassilis Z. Antonopoulos ◽  
Zafiris G. Papazafiriou
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Porous Media ◽  
Mass Transport ◽  
Water Flow ◽  
Transport Equations ◽  
Saturated Porous Media ◽  
The Finite Element Method ◽  
One Dimensional ◽  
Flow And Mass Transport

scholarly journals Finite Element Analysis of Thermoelastic Contact Stability

1994 ◽  
Vol 61 (4) ◽  
pp. 919-922 ◽  
Author(s):  
Taein Yeo ◽  
J. R. Barber
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Steady State ◽  
Eigenvalue Problem ◽  
Linear Perturbation ◽  
Dimensional System ◽  
The Finite Element Method ◽  
One Dimensional ◽  
Thermoelastic Contact ◽  
Element Method

When heat is conducted across an interface between two dissimilar materials, theimoelastic distortion affects the contact pressure distribution. The existence of a pressure-sensitive thermal contact resistance at the interface can cause such systems to be unstable in the steady-state. Stability analysis for thermoelastic contact has been conducted by linear perturbation methods for one-dimensional and simple two-dimensional geometries, but analytical solutions become very complicated for finite geometries. A method is therefore proposed in which the finite element method is used to reduce the stability problem to an eigenvalue problem. The linearity of the underlying perturbation problem enables us to conclude that solutions can be obtained in separated-variable form with exponential variation in time. This factor can therefore be removed from the governing equations and the finite element method is used to obtain a time-independent set of homogeneous equations in which the exponential growth rate appears as a linear parameter. We therefore obtain a linear eigenvalue problem and stability of the system requires that all the resulting eigenvalues should have negative real part. The method is discussed in application to the simple one-dimensional system of two contacting rods. The results show good agreement with previous analytical investigations and give additional information about the migration of eigenvalues in the complex plane as the steady-state heat flux is varied.

Semi-analytical finite element method for simulating chemical dissolution-front instability problems in fluid-saturated porous media

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Chongbin Zhao ◽  
B.E. Hobbs ◽  
Alison Ord
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Porous Media ◽  
Chemical Dissolution ◽  
Saturated Porous Media ◽  
Content Type ◽  
Front Instability ◽  
Fluid Saturated Porous Media ◽  
Dissolution Front ◽  
Element Method

PurposeThe objective of this paper is to develop a semi-analytical finite element method for solving chemical dissolution-front instability problems in fluid-saturated porous media.Design/methodology/approachThe porosity, horizontal and vertical components of the pore-fluid velocity and solute concentration are selected as four fundamental unknown variables for describing chemical dissolution-front instability problems in fluid-saturated porous media. To avoid the use of numerical integration, analytical solutions for the property matrices of a rectangular element are precisely derived in a purely mathematical manner. This means that the proposed finite element method is a kind of semi-analytical method. The column pivot element solver is used to solve the resulting finite element equations of the chemical dissolution-front instability problem.FindingsThe direct use of horizontal and vertical components of the pore-fluid velocity as fundamental unknown variables can improve the accuracy of the related numerical solution. The column pivot element solver is useful for solving the finite element equations of a chemical dissolution-front instability problem. The proposed semi-analytical finite element method can produce highly accurate numerical solutions for simulating chemical dissolution-front instability problems in fluid-saturated porous media.Originality/valueAnalytical solutions for the property matrices of a rectangular element are precisely derived for solving chemical dissolution-front instability problems in fluid-saturated porous media. The proposed semi-analytical finite element method provides a useful way for understanding the underlying dynamic mechanisms of the washing land method involved in the contaminated land remediation.

scholarly journals The use of the finite-element method for the simulation of ground water flow

1988 ◽  
Vol 7 (4) ◽  
pp. 174-183
Author(s):  
G. J. Van Tonder ◽  
J. F. Botha
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Ground Water ◽  
Water Flow ◽  
Flow Model ◽  
The Finite Element Method ◽  
Ground Water Flow ◽  
Available Information ◽  
Good Flow ◽  
Element Method

The present investigation is mostly concerned with the contribution that the finite-element method can make towards the simulation of ground water flow. After a brief introduction to the finite element method, it is applied to the Grootfontein dolomitic aquifer near Mafikeng/Mmabatho. This aquifer yields water for irrigation purposes as well as water for the township. By utilizing the available information a good flow model was constructed for this aquifer. The model is considered calibrated and verificated.

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