scholarly journals On the Stream Function-Vorticity Finite Element Formulation for Incompressible Flow in Porous Media

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Abdellatif Agouzal ◽  
Karam Allali ◽  
Siham Binna
Keyword(s):  
Finite Element ◽  
Porous Media ◽  
Stream Function ◽  
Incompressible Flow ◽  
Equations Of Motion ◽  
Finite Element Formulation ◽  
Flow In Porous Media ◽  
Darcy Law ◽  
Element Formulation ◽  
Discrete Problem

Stream function-vorticity finite element formulation for incompressible flow in porous media is presented. The model consists of the heat equation, the equation for the concentration, and the equations of motion under the Darcy law. The existence of solution for the discrete problem is established. Optimal a priori error estimates are given.

A two-scale finite element formulation of Stokes flow in porous media

2013 ◽  
Vol 261-262 ◽  
pp. 96-104 ◽  
Author(s):  
Carl Sandström ◽  
Fredrik Larsson ◽  
Kenneth Runesson ◽  
Håkan Johansson
Keyword(s):  
Finite Element ◽  
Porous Media ◽  
Stokes Flow ◽  
Finite Element Formulation ◽  
Flow In Porous Media ◽  
Element Formulation

Dynamics of Thick Viscoelastic Beams

1997 ◽  
Vol 119 (3) ◽  
pp. 273-278 ◽  
Author(s):  
A. R. Johnson ◽  
A. Tessler ◽  
M. Dambach
Keyword(s):  
Finite Element ◽  
Virtual Work ◽  
Equations Of Motion ◽  
Constitutive Law ◽  
Finite Element Formulation ◽  
Internal Variables ◽  
Element Formulation ◽  
Modal Interactions ◽  
Cantilevered Beam ◽  
Thick Beam

A viscoelastic higher-order thick beam finite element formulation is extended to include elastodynamic deformations. The material constitutive law is a special differential form of the Maxwell solid, which employs viscous strains as internal variables to determine the viscous stresses. The total time-dependent stress is the superposition of its elastic and viscous components. In the constitutive model, the elastic strains and the conjugate viscous strains are coupled through a system of first-order ordinary differential equations. The use of the internal strain variables allows for a convenient finite element formulation. The elastodynamic equations of motion are derived from the virtual work principle. Computational examples are carried out for a thick orthotropic cantilevered beam. Relaxation, creep, relaxation followed by free damped vibrations, and damping related modal interactions are discussed.

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