scholarly journals Analytic and Numerical Solutions of Couette Flow Problem: A Comparative Study

2017 ◽  
Vol 12 (1) ◽  
pp. 105-113
Author(s):  
Dhak Bahadur Thapa ◽  
Kedar Nath Uprety
Keyword(s):  
Differential Equation ◽  
Couette Flow ◽  
Numerical Solutions ◽  
Flow Problem ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Parabolic Partial Differential Equation ◽  
Navier Stokes Equations ◽  
One Dimensional ◽  
Nicolson Scheme

In this work, an incompressible viscous Couette flow is derived by simplifying the Navier-Stokes equations and the resulting one dimensional linear parabolic partial differential equation is solved numerically employing a second order finit difference Crank-Nicolson scheme. The numerical solution and the exact solution are presented graphically.Journal of the Institute of Engineering, 2016, 12(1): 105-113

scholarly journals NEWTONIAN FLOW IN CONVERGING-DIVERGING CAPILLARIES

2013 ◽  
Vol 04 (03) ◽  
pp. 1350011 ◽  
Author(s):  
TAHA SOCHI
Keyword(s):  
Numerical Solutions ◽  
Stokes Equations ◽  
Volumetric Flow Rate ◽  
Navier Stokes ◽  
Lubrication Approximation ◽  
Newtonian Flow ◽  
Navier Stokes Equations ◽  
One Dimensional ◽  
The One ◽  
Analytical Expressions

The one-dimensional Navier–Stokes equations are used to derive analytical expressions for the relation between pressure and volumetric flow rate in capillaries of five different converging-diverging axisymmetric geometries for Newtonian fluids. The results are compared to previously derived expressions for the same geometries using the lubrication approximation. The results of the one-dimensional Navier–Stokes are identical to those obtained from the lubrication approximation within a nondimensional numerical factor. The derived flow expressions have also been validated by comparison to numerical solutions obtained from discretization with numerical integration. Moreover, they have been certified by testing the convergence of solutions as the converging-diverging geometries approach the limiting straight geometry.

scholarly journals Calculation of the pressure on the valves of a sluice

1997 ◽  
Vol 19 (3) ◽  
pp. 25-34
Author(s):  
Tran Gia Lich ◽  
Le Kim Luat ◽  
Han Quoc Trinh
Keyword(s):  
Numerical Method ◽  
Method Of Characteristics ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Sweep Method ◽  
Navier Stokes Equations ◽  
One Dimensional ◽  
Interior Points

This paper is devoted to a numerical method for calculating the pressure on the vertical two-dimensional valve basing on Navier-Stokes equations. Numerical solutions at interior points are established by splitting Navie-Stokes unsteady two-dimensional equations into two unsteady one-dimensional equations. An implicit scheme is obtained and the solution for these equations is established by the double sweep method. The values at the boundary points are calculated by the method of characteristics.

A numerical study of the interaction between unsteay free-stream disturbances and localized variations in surface geometry

1989 ◽  
Vol 209 ◽  
pp. 285-308 ◽  
Author(s):  
R. J. Bodonyi ◽  
W. J. C. Welch ◽  
P. W. Duck ◽  
M. Tadjfar
Keyword(s):  
Numerical Solutions ◽  
Free Stream ◽  
Stokes Equations ◽  
Numerical Study ◽  
Navier Stokes ◽  
Surface Geometry ◽  
Navier Stokes Equations ◽  
S Waves ◽  
Tollmien Schlichting

A numerical study of the generation of Tollmien-Schlichting (T–S) waves due to the interaction between a small free-stream disturbance and a small localized variation of the surface geometry has been carried out using both finite–difference and spectral methods. The nonlinear steady flow is of the viscous–inviscid interactive type while the unsteady disturbed flow is assumed to be governed by the Navier–Stokes equations linearized about this flow. Numerical solutions illustrate the growth or decay of the T–S waves generated by the interaction between the free-stream disturbance and the surface distortion, depending on the value of the scaled Strouhal number. An important result of this receptivity problem is the numerical determination of the amplitude of the T–S waves.

NUMERICAL SOLUTIONS OF 2D AND 3D SLAMMING PROBLEMS

2021 ◽  
Vol 153 (A2) ◽  
Author(s):  
Q Yang ◽  
W Qiu
Keyword(s):  
Free Surface ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Type Equation ◽  
The Body ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Highly Nonlinear ◽  
2D And 3D

Slamming forces on 2D and 3D bodies have been computed based on a CIP method. The highly nonlinear water entry problem governed by the Navier-Stokes equations was solved by a CIP based finite difference method on a fixed Cartesian grid. In the computation, a compact upwind scheme was employed for the advection calculations and a pressure-based algorithm was applied to treat the multiple phases. The free surface and the body boundaries were captured using density functions. For the pressure calculation, a Poisson-type equation was solved at each time step by the conjugate gradient iterative method. Validation studies were carried out for 2D wedges with various deadrise angles ranging from 0 to 60 degrees at constant vertical velocity. In the cases of wedges with small deadrise angles, the compressibility of air between the bottom of the wedge and the free surface was modelled. Studies were also extended to 3D bodies, such as a sphere, a cylinder and a catamaran, entering calm water. Computed pressures, free surface elevations and hydrodynamic forces were compared with experimental data and the numerical solutions by other methods.

Pulsatile Waterhammer Subject to Laminar Friction

1972 ◽  
Vol 94 (2) ◽  
pp. 467-472 ◽  
Author(s):  
D. A. P. Jayasinghe ◽  
H. J. Leutheusser
Keyword(s):  
Stokes Equations ◽  
Fluid Motion ◽  
Present Theory ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
One Dimensional ◽  
Arbitrary Velocity ◽  
Velocity Input ◽  
Special Case ◽  
Signalling Problem

This paper deals with elastic waves which may be generated in a fluid by the sudden movement of a flow boundary. In particular, an analysis of the classical piston, or signalling problem is presented for the special case of arbitrary velocity input into a stationary fluid contained in a circular, semi-infinite waveguide. The decay of the pulse, as well as the resulting flow development in the inlet region of the pipe are analyzed by means of an asymptotic expansion of the suitably nondimensionalized Navier-Stokes equations for a compressible, nonheat-conducting Newtonian fluid. The results differ significantly from those of the more conventional one-dimensional approach based on the so-called telegrapher’s equation of mathematical physics. The present theory realistically predicts the growth of a boundary layer both in time and position and, hence, it appears to represent the transient fluid motion in a manner which is physically more appealing.

scholarly journals Disconnected stationary solutions for 3D Kolmogorov flow problem: preliminary results

2021 ◽  
Vol 2090 (1) ◽  
pp. 012046
Author(s):  
Nikolay M. Evstigneev
Keyword(s):  
Flow Problem ◽  
Stokes Equations ◽  
Continuation Method ◽  
Fourier Method ◽  
Stationary Solutions ◽  
Navier Stokes ◽  
System Of Nonlinear Equations ◽  
Arc Length ◽  
Navier Stokes Equations ◽  
Numerical Bifurcation

Abstract The extension of the classical A.N. Kolmogorov’s flow problem for the stationary 3D Navier-Stokes equations on a stretched torus for velocity vector function is considered. A spectral Fourier method with the Leray projection is used to solve the problem numerically. The resulting system of nonlinear equations is used to perform numerical bifurcation analysis. The problem is analyzed by constructing solution curves in the parameter-phase space using previously developed deflated pseudo arc-length continuation method. Disconnected solutions from the main solution branch are found. These results are preliminary and shall be generalized elsewhere.

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