Approximate Analytical Solution of Non-linear Equation in one Dimensional Imbibitions Phenomenon in Homogeneous Porous Media by Homotopy Perturbation Method

Desai, Khyati R.; Pradhan, V. H.; Daga, Amruta; Mistry, P. R.

doi:10.1016/j.proeng.2015.11.448

Cited by 5 publications

(2 citation statements)

References 8 publications

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“…where ( ) is a Lagrange multiplier (He 2007) which can be readily identified as = − 1 stated above. Substituting this value of the Lagrange's multiplier into functional (10) gives the iteration formula Following VHPM (Daga and Pradhan 2014a, b;Desai et al 2015) as stated above, we have Comparing the coefficient of like powers of p, we obtain the following components Proceeding in similar manner, we can obtain further approximations.…”

Section: Numerical Solution (B-spline Finite Element Method)mentioning

confidence: 99%

New analytical solution for stream–aquifer interaction under constant replenishment

2018

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In the present paper, approximate analytical solutions for flow in unconfined aquifers with streams are obtained assuming one-dimensional horizontal groundwater flow in homogeneous and isotropic aquifer with recharge effect using variational homotopy perturbation method which is a combination of variational iteration method and homotopy perturbation method. The governing nonlinear Boussinesq equation is obtained by using a basic principle of conservation of mass followed by Dupuit's assumptions. Sensitivity of the parameters has been analyzed. The obtained approximate analytical solutions are numerically validated. The present analytical method is reliable and can be equally well applied to other nonlinear equations arising in the stream-aquifer interaction problems.Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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Section: Numerical Solution (B-spline Finite Element Method)mentioning

confidence: 99%

New analytical solution for stream–aquifer interaction under constant replenishment

2018

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“…These can be determined by the statistical treatment. Darcy's law (2003), the equation of continuity and certain basic assumptions yields given a nonlinear partial differential equation for the motion of saturation of injecting fluid [5].…”

Section: Introductionmentioning

confidence: 99%

Analytical Study of Instability Phenomenon Using Laplace Transform

Kaushal¹,

Pravin²

2022

MMEP

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In the present work, demonstrate the analytical method to analyze the instability phenomenon by using Laplace transform. For the analysis of instability two phase immiscible flow through the homogenous porous media is adopted. Fingering method is used to develop the Burger’s equation. Which is used to obtain the saturation of water by Laplace transform method. The analytical results show that the saturation of water decreases with an increase in injected fluid and time. The obtained analytical results also satisfied and confirmed from the simulated results that shows the saturation of water.

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Simulation of Counter-Current Imbibition Phenomenon with Corey’s Model in Double Phase Flow Through Heterogeneous Porous Medium with Capillary Pressure

Patel

Meher

2017

Int. J. Appl. Comput. Math

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Approximate Analytical Solution of Non-linear Equation in one Dimensional Imbibitions Phenomenon in Homogeneous Porous Media by Homotopy Perturbation Method

Cited by 5 publications

References 8 publications

New analytical solution for stream–aquifer interaction under constant replenishment

New analytical solution for stream–aquifer interaction under constant replenishment

Analytical Study of Instability Phenomenon Using Laplace Transform

Simulation of Counter-Current Imbibition Phenomenon with Corey’s Model in Double Phase Flow Through Heterogeneous Porous Medium with Capillary Pressure

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