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.

scholarly journals An Axisymmetric Squeezing Fluid Flow between the Two Infinite Parallel Plates in a Porous Medium Channel

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
S. Islam ◽  
Hamid Khan ◽  
Inayat Ali Shah ◽  
Gul Zaman
Keyword(s):  
Differential Equation ◽  
Porous Medium ◽  
Fluid Flow ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Parallel Plates ◽  
Transform Method ◽  
Navier Stokes Equations ◽  
Differential Transform ◽  
Fluid Parameters

The flow between two large parallel plates approaching each other symmetrically in a porous medium is studied. The Navier-Stokes equations have been transformed into an ordinary nonlinear differential equation using a transformationψ(r,z)=r2F(z). Solution to the problem is obtained by using differential transform method (DTM) by varying different Newtonian fluid parameters and permeability of the porous medium. Result for the stream function is presented. Validity of the solutions is confirmed by evaluating the residual in each case, and the proposed scheme gives excellent and reliable results. The influence of different parameters on the flow has been discussed and presented through graphs.

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.

scholarly journals A New Approximate Analytical Solutions for Two- and Three-Dimensional Unsteady Viscous Incompressible Flows by Using the Kinetically Reduced Local Navier-Stokes Equations

2019 ◽  
Vol 2019 ◽  
pp. 1-19
Author(s):  
Abdul-Sattar J. Al-Saif ◽  
Assma J. Harfash
Keyword(s):  
Analytical Solutions ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Transform Method ◽  
Navier Stokes Equations ◽  
Good Convergence ◽  
Flow Problems ◽  
Approximate Analytical Solutions

In this work, the kinetically reduced local Navier-Stokes equations are applied to the simulation of two- and three-dimensional unsteady viscous incompressible flow problems. The reduced differential transform method is used to find the new approximate analytical solutions of these flow problems. The new technique has been tested by using four selected multidimensional unsteady flow problems: two- and three-dimensional Taylor decaying vortices flow, Kovasznay flow, and three-dimensional Beltrami flow. The convergence analysis was discussed for this approach. The numerical results obtained by this approach are compared with other results that are available in previous works. Our results show that this method is efficient to provide new approximate analytic solutions. Moreover, we found that it has highly precise solutions with good convergence, less time consuming, being easily implemented for high Reynolds numbers, and low Mach numbers.

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.

Effects of stator splitter blades on aerodynamic performance of a single-stage transonic axial compressor

2020 ◽  
Vol 14 (4) ◽  
pp. 7369-7378
Author(s):  
Ky-Quang Pham ◽  
Xuan-Truong Le ◽  
Cong-Truong Dinh
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Aerodynamic Performance ◽  
Numerical Results ◽  
Single Stage ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Operating Stability ◽  
Length Coverage

Splitter blades located between stator blades in a single-stage axial compressor were proposed and investigated in this work to find their effects on aerodynamic performance and operating stability. Aerodynamic performance of the compressor was evaluated using three-dimensional Reynolds-averaged Navier-Stokes equations using the k-e turbulence model with a scalable wall function. The numerical results for the typical performance parameters without stator splitter blades were validated in comparison with experimental data. The numerical results of a parametric study using four geometric parameters (chord length, coverage angle, height and position) of the stator splitter blades showed that the operational stability of the single-stage axial compressor enhances remarkably using the stator splitter blades. The splitters were effective in suppressing flow separation in the stator domain of the compressor at near-stall condition which affects considerably the aerodynamic performance of the compressor.

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