Analytical Approach to a Slowly Deforming Channel Flow with Weak Permeability

2010 ◽  
Vol 65 (12) ◽  
pp. 1033-1038 ◽  
Author(s):  
Syed Tauseef Mohyud-Din ◽  
Ahmet Yıldırım ◽  
Sefa Anıl Sezer
Keyword(s):  
Series Solution ◽  
Analytical Approach ◽  
Homotopy Perturbation Method ◽  
Stokes Equations ◽  
Rectangular Channel ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Remarkable Improvement ◽  
Homotopy Perturbation ◽  
Expanding Or Contracting Walls

In this paper, we develop the analytical solution of the Navier-Stokes equations for a semi-infinite rectangular channel with porous and uniformly expanding or contracting walls by employing the homotopy perturbation method (HPM). The series solution of the governing problem is obtained. Some examples have been included. The results so obtained are compared with the existing literature and a remarkable improvement leads to an excellent agreement with the numerical results.

NEW ANALYTICAL SOLUTION OF THE THREE-DIMENSIONAL NAVIER–STOKES EQUATIONS

2009 ◽  
Vol 23 (26) ◽  
pp. 3147-3155 ◽  
Author(s):  
MOHAMMAD MEHDI RASHIDI ◽  
GANJI DOMAIRRY
Keyword(s):  
Homotopy Perturbation Method ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Rotating Disk ◽  
Navier Stokes ◽  
Transform Method ◽  
Navier Stokes Equations ◽  
Homotopy Perturbation ◽  
Differential Transform ◽  
Conditions At Infinity

The purpose of this study is to implement a new analytical method (the DTM-Padé technique, which is a combination of the differential transform method (DTM) and the Padé approximation) for solving Navier–Stokes equations. In this letter, we will consider the DTM, the homotopy perturbation method (HPM) and the Padé approximant for finding analytical solutions of the three-dimensional viscous flow near an infinite rotating disk. The solutions are compared with the numerical (fourth-order Runge–Kutta) solution. The results illustrate that the application of the Padé approximants in the DTM and HPM is an appropriate method in solving the Navier–Stokes equations with the boundary conditions at infinity. On the other hand, the convergence of the obtained series from DTM-Padé is greater than HPM-Padé.

Comparison of iterative methods by solving nonlinear Sturm-Liouville, Burgers and Navier-Stokes equations

Open Physics ◽  
2012 ◽  
Vol 10 (4) ◽  
Author(s):  
Alireza Golmankhaneh ◽  
Tuhid Khatuni ◽  
Neda Porghoveh ◽  
Dumitru Baleanu
Keyword(s):  
Iterative Method ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Homotopy Perturbation ◽  
Approximate Analytical Solutions ◽  
Sturm Liouville ◽  
Variational Iterative Method

AbstractIn this manuscript the homotopy perturbation method, the new iterative method, and the variational iterative method have been successively used to obtain approximate analytical solutions of nonlinear Sturm-Liouville, Navier-Stokes and Burgers’ equations. It is shown that the homotopy perturbation method gives approximate analytical solution near to the exact one. We have illustrated the obtained results by sketching the graph of the solutions.

scholarly journals A COMPARISON OF THE ADOMIAN AND HOMOTOPY PERTURBATION METHODS IN SOLVING THE PROBLEM OF SQUEEZING FLOW BETWEEN TWO CIRCULAR PLATES

2010 ◽  
Vol 15 (4) ◽  
pp. 491-504 ◽  
Author(s):  
Abdul M. Siddiqui ◽  
Tahira Haroon ◽  
Saira Bhatti ◽  
Ali R. Ansari
Keyword(s):  
Stokes Equations ◽  
Adomian Decomposition Method ◽  
Nonlinear Problems ◽  
Computational Effort ◽  
Navier Stokes ◽  
Squeezing Flow ◽  
Circular Plates ◽  
Navier Stokes Equations ◽  
Homotopy Perturbation ◽  
Adomian Decomposition

The objective of this paper is to compare two methods employed for solving nonlinear problems, namely the Adomian Decomposition Method (ADM) and the Homotopy Perturbation Method (HPM). To this effect we solve the Navier‐Stokes equations for the unsteady flow between two circular plates approaching each other symmetrically. The comparison between HPM and ADM is bench‐marked against a numerical solution. The results show that the ADM is more reliable and efficient than HPM from a computational viewpoint. The ADM requires slightly more computational effort than the HPM, but it yields more accurate results than the HPM.

scholarly journals A reliable algorithm for time-fractional Navier-Stokes equations via Laplace transform

2019 ◽  
Vol 8 (1) ◽  
pp. 695-701 ◽  
Author(s):  
Amit Prakash ◽  
Doddabhadrappla Gowda Prakasha ◽  
Pundikala Veeresha
Keyword(s):  
Fluid Flow ◽  
Viscous Fluid ◽  
Fractional Derivative ◽  
Series Solution ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Viscous Fluid Flow ◽  
Analysis Scheme ◽  
Homotopy Analysis

Abstract In this paper, numerical solution of fractional order Navier-Stokes equations in unsteady viscous fluid flow is found using q-homotopy analysis transform scheme. Fractional derivative is considered in Caputo sense. The proposed technique is a blend of q-homotopy analysis scheme and transform of Laplace. It executes well in efficiency and provides h-curves that show convergence range of series solution.

Interaction of a Single Large Wave With a Tall Fixed Structure: A Numerical Study

2003 ◽  
Author(s):  
Remus M. Ciobotaru ◽  
Razvan Bidoae ◽  
Peter E. Raad
Keyword(s):  
Surface Deformation ◽  
Stokes Equations ◽  
Numerical Study ◽  
Rectangular Channel ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Large Wave ◽  
Free Surface Deformation ◽  
Fixed Structure ◽  
The University

This paper presents a numerical study of the interaction of a single large wave with tall fixed structures in a rectangular channel. Three different shapes, a circle, a square and a rhombus, have been considered for the fixed structure. The numerical results are compared with experimental data available from experiments performed at the University of Washington, Seattle. The hydrodynamic force impinging on the vertical structure for different water impoundments behind the gate is considered and discussed. The motion of the fluid flow around the fixed structure is based on the solution of the complete Navier-Stokes equations. The free surface deformation is solved by the use of the Eulerian-Lagrangian Marker and Micro Cell (ELMMC) method.

Reynolds Stress Modeling for Drag Reducing Viscoelastic Flows

2003 ◽  
Author(s):  
Richard Leighton ◽  
David T. Walker ◽  
Todd Stephens ◽  
Gordon Garwood
Keyword(s):  
Reynolds Stress ◽  
Stokes Equations ◽  
Equations Of Motion ◽  
Rectangular Channel ◽  
Equation Model ◽  
Navier Stokes ◽  
Viscoelastic Flows ◽  
Navier Stokes Equations ◽  
The Mean ◽  
Conformation Tensor

A Reynolds-stress transport equation model for turbulent drag-reducing viscoelastic flows, such as that which occurs for dilute polymer solutions, is presented. The approach relies on an extended set of Reynolds-Averaged Navier-Stokes equations which incorporate additional polymer stresses. The polymer stresses are specified in terms of the mean polymer conformation tensor using the FENE-P dumbbell model. The mean conformation tensor equation is solved in a coupled manner along with the Navier-Stokes equations. The presence of the polymer stresses in the equations of motion results in additional explicit polymer terms in the Reynolds-stress transport equations, as well as implicit polymer effects in the pressure-strain redistribution term. Models for both the explicit and implicit effects have been developed and implemented in a code suitable for boundary layer, rectangular channel and pipe-flow geometries. Calibration and validation is has been carried out using results from recent direct numerical simulation of viscoelastic turbulent flow.

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