scholarly journals Mathematical Model and Solution for Fingering Phenomenon in Double Phase Flow through Homogeneous Porous Media

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Piyush R. Mistry ◽  
Vikas H. Pradhan ◽  
Khyati R. Desai
Keyword(s):  
Mathematical Model ◽  
Porous Media ◽  
Iteration Method ◽  
Physical Phenomenon ◽  
Nonlinear Partial Differential Equation ◽  
Variational Iteration Method ◽  
Phase Flow ◽  
Variational Iteration ◽  
Double Phase ◽  
Flow Through

The present paper analytically discusses the phenomenon of fingering in double phase flow through homogenous porous media by using variational iteration method. Fingering phenomenon is a physical phenomenon which occurs when a fluid contained in a porous medium is displaced by another of lesser viscosity which frequently occurred in problems of petroleum technology. In the current investigation a mathematical model is presented for the fingering phenomenon under certain simplified assumptions. An approximate analytical solution of the governing nonlinear partial differential equation is obtained using variational iteration method with the use of Mathematica software.

The Variational-Iteration Method to Solve the Nonlinear Boltzmann Equation

2008 ◽  
Vol 63 (3-4) ◽  
pp. 131-139 ◽  
Author(s):  
Essam M. Abulwafa ◽  
Mohammed A. Abdou ◽  
Aber H. Mahmoud
Keyword(s):  
Differential Equation ◽  
Distribution Function ◽  
Boltzmann Equation ◽  
Generating Function ◽  
Iteration Method ◽  
Nonlinear Partial Differential Equation ◽  
Variational Iteration Method ◽  
Inhomogeneous Media ◽  
Nonlinear Boltzmann Equation ◽  
Variational Iteration

The time-dependent nonlinear Boltzmann equation, which describes the time evolution of a single-particle distribution in a dilute gas of particles interacting only through binary collisions, is considered for spatially homogeneous and inhomogeneous media without external force and energy source. The nonlinear Boltzmann equation is converted to a nonlinear partial differential equation for the generating function of the moments of the distribution function. The variational-iteration method derived by He is used to solve the nonlinear differential equation of the generating function. The moments for both homogeneous and inhomogeneous media are calculated and represented graphically as functions of space and time. The distribution function is calculated from its moments using the cosine Fourier transformation. The distribution functions for the homogeneous and inhomogeneous media are represented graphically as functions of position and time.

scholarly journals Approximate Solutions for Local Fractional Linear Transport Equations Arising in Fractal Porous Media

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Meng Li ◽  
Xiao-Feng Hui ◽  
Carlo Cattani ◽  
Xiao-Jun Yang ◽  
Yang Zhao
Keyword(s):  
Porous Media ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
Transport Equations ◽  
Nondifferentiable Functions ◽  
Linear Transport ◽  
Variational Iteration

We investigate the local fractional linear transport equations arising in fractal porous media by using the local fractional variational iteration method. Their approximate solutions within the nondifferentiable functions are obtained and their graphs are also shown.

scholarly journals Variational Iteration Method and Differential Transformation Method for Solving the SEIR Epidemic Model

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
A. Harir ◽  
S. Melliani ◽  
H. El Harfi ◽  
L. S. Chadli
Keyword(s):  
Mathematical Model ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Transformation Method ◽  
Differential Transformation Method ◽  
Nonlinear Ordinary Differential Equations ◽  
Nonlinear Odes ◽  
Differential Transformation ◽  
Variational Iteration ◽  
The Mathematical Model

The aim of the present study is to analyze and find a solution for the model of nonlinear ordinary differential equations (ODEs) describing the so-called coronavirus (COVID-19), a deadly and most parlous virus. The mathematical model based on four nonlinear ODEs is presented, and the corresponding numerical results are studied by applying the variational iteration method (VIM) and differential transformation method (DTM).

scholarly journals New analytical solution for natural convection of Darcian fluid in porous media prescribed surface heat flux

2011 ◽  
Vol 15 (suppl. 2) ◽  
pp. 221-227 ◽  
Author(s):  
Domiry Ganji ◽  
Hasan Sajjadi
Keyword(s):  
Heat Flux ◽  
Porous Media ◽  
Differential Equations ◽  
Iteration Method ◽  
Surface Heat Flux ◽  
Nonlinear Differential Equations ◽  
Variational Iteration Method ◽  
Surface Heat ◽  
Variational Iteration ◽  
He’S Variational Iteration Method

A new analytical method called He's Variational Iteration Method is introduced to be applied to solve nonlinear equations. In this method, general Lagrange multipliers are introduced to construct correction functional for the problems. It is strongly and simply capable of solving a large class of linear or nonlinear differential equations without the tangible restriction of sensitivity to the degree of the nonlinear term and also is very user friend because it reduces the size of calculations besides; its iterations are direct and straightforward. In this paper the powerful method called Variational Iteration Method is used to obtain the solution for a nonlinear Ordinary Differential Equations that often appear in boundary layers problems arising in heat and mass transfer which these kinds of the equations contain infinity boundary condition. The boundary layer approximations of fluid flow and heat transfer of vertical full cone embedded in porous media give us the similarity solution for full cone subjected to surface heat flux boundary conditions. The obtained Variational Iteration Method solution in comparison with the numerical ones represents a remarkable accuracy.

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