Time-dependent solutions of the Navier–Stokes equations for spatially-uniform velocity gradients

1994 ◽  
Vol 124 (1) ◽  
pp. 127-136 ◽  
Author(s):  
A. D. D. Craik
Keyword(s):  
Fluid Flow ◽  
Incompressible Fluid ◽  
Stokes Equations ◽  
Time Dependent ◽  
Navier Stokes ◽  
Incompressible Fluid Flow ◽  
Navier Stokes Equations ◽  
Temporal Behaviour ◽  
Uniform Velocity ◽  
Velocity Gradients

Classes of exact solutions of the Navier–Stokes equations for incompressible fluid flow are explored. These have spatially-uniform velocity gradients at each instant, but often display complex temporal behaviour. Particular illustrative cases are described and related to previously-known solutions.

Time delay and Lagrangian approximation for Navier–Stokes flow

Analysis ◽  
2015 ◽  
Vol 35 (4) ◽  
Author(s):  
Nazgul Asanalieva ◽  
Carolin Heutling ◽  
Werner Varnhorn
Keyword(s):  
Fluid Flow ◽  
Time Delay ◽  
Incompressible Fluid ◽  
Stokes Flow ◽  
Stokes Equations ◽  
Viscous Incompressible Fluid ◽  
Navier Stokes ◽  
Incompressible Fluid Flow ◽  
Navier Stokes Equations

AbstractWe consider the nonstationary nonlinear Navier–Stokes equations describing the motion of a viscous incompressible fluid flow for

scholarly journals NUMERICAL SIMULATION OF LID-DRIVEN CAVITY FLOW BY ISOGEOMETRIC ANALYSIS

2021 ◽  
Vol 61 (SI) ◽  
pp. 33-48
Author(s):  
Bohumír Bastl ◽  
Marek Brandner ◽  
Jiří Egermaier ◽  
Hana Horníková ◽  
Kristýna Michálková ◽  
...  
Keyword(s):  
Fluid Flow ◽  
Incompressible Fluid ◽  
Isogeometric Analysis ◽  
Stokes Equations ◽  
Cavity Flow ◽  
Navier Stokes ◽  
Incompressible Fluid Flow ◽  
Navier Stokes Equations ◽  
Flow Solver ◽  
Driven Cavity

In this paper, we present numerical results obtained by an in-house incompressible fluid flow solver based on isogeometric analysis (IgA) for the standard benchmark problem for incompressible fluid flow simulation – lid-driven cavity flow. The steady Navier-Stokes equations are solved in their velocity-pressure formulation and we consider only inf-sup stable pairs of B-spline discretization spaces. The main aim of the paper is to compare the results from our IgA-based flow solver with the results obtained by a standard package based on finite element method with respect to degrees of freedom and stability of the solution. Further, the effectiveness of the recently introduced rIgA method for the steady Navier-Stokes equations is studied.The authors dedicate the paper to Professor K. Kozel on the occasion of his 80th birthday.

scholarly journals Analytical Solutions for Navier-Stokes Equations in the Cylindrical Coordinates

2012 ◽  
Vol 2 ◽  
pp. 16-23 ◽  
Author(s):  
V. Adanhounme ◽  
A. Adomou ◽  
F.P. Codo
Keyword(s):  
Temperature Field ◽  
Fluid Flow ◽  
Incompressible Fluid ◽  
Heat Transport ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Incompressible Fluid Flow ◽  
Cylindrical Coordinates ◽  
Navier Stokes Equations ◽  
Vorticity Vector

We consider the problem of convective heat transport in the incompressible fluid flow and the motion of the fluid in the cylinder which is described by the Navier-Stokes equations with the heat equation.The exact solutions of the Navier-Stokes equations, the temperature field and the vorticity vector are obtained.

scholarly journals Exact Solution of 3D Navier–Stokes Equations

2020 ◽  
pp. 306-313
Author(s):  
Alexander V. Koptev
Keyword(s):  
Exact Solution ◽  
Fluid Flow ◽  
Incompressible Fluid ◽  
Exact Solutions ◽  
Stokes Equations ◽  
First Integral ◽  
Navier Stokes ◽  
Incompressible Fluid Flow ◽  
Navier Stokes Equations ◽  
Particular Solutions

Procedure for constructing exact solutions of 3D Navier–Stokes equations for an incompressible fluid flow is proposed. It is based on the relations representing the previously obtained first integral of the Navier–Stokes equations. A primary generator of particular solutions is proposed. It is used to obtain new classes of exact solutions

Numerical Computation of Fluid Flow and Heat Transfer in Microchannels

2005 ◽  
Author(s):  
Ningli Liu ◽  
Rene Chevray ◽  
Gerald A. Domoto ◽  
Elias Panides
Keyword(s):  
Heat Transfer ◽  
Fluid Flow ◽  
Energy Equation ◽  
Stokes Equations ◽  
Numerical Approach ◽  
Time Dependent ◽  
Navier Stokes ◽  
Temperature Profiles ◽  
Navier Stokes Equations ◽  
Flow And Heat Transfer

A finite difference numerical approach for solving slightly compressible, time-dependent, viscous laminar flow is presented in this study. Simplified system of Navier-Stokes equations and energy equation are employed in the study in order to perform more efficient numerical calculations. Fluid flow and heat transfer phenomena in two dimensional microchannels are illustrated numerically in this paper. This numerical approach provides a complete numerical simulation of the development of the fluid flow and the temperature profiles through multi-dimensional microchannels.

scholarly journals Kolmogorov's dissipation number and the number of degrees of freedom for the 3D Navier–Stokes equations

2019 ◽  
Vol 149 (2) ◽  
pp. 429-446
Author(s):  
Alexey Cheskidov ◽  
Mimi Dai
Keyword(s):  
Fluid Flow ◽  
Degrees Of Freedom ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Critical Value ◽  
Time Dependent ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
All Solutions ◽  
Time Average

AbstractKolmogorov's theory of turbulence predicts that only wavenumbers below some critical value, called Kolmogorov's dissipation number, are essential to describe the evolution of a three-dimensional (3D) fluid flow. A determining wavenumber, first introduced by Foias and Prodi for the 2D Navier–Stokes equations, is a mathematical analogue of Kolmogorov's number. The purpose of this paper is to prove the existence of a time-dependent determining wavenumber for the 3D Navier–Stokes equations whose time average is bounded by Kolmogorov's dissipation wavenumber for all solutions on the global attractor whose intermittency is not extreme.

scholarly journals Incompressible Fluid Flow Computation in an Arbitrary Two-dimensional Region on Nonstaggered Grids

2005 ◽  
Vol 5 (3) ◽  
pp. 242-258
Author(s):  
Mikhail Chuiko ◽  
Andrei Lapanik ◽  
Ricardo H. Nochetto
Keyword(s):  
Fluid Flow ◽  
Stokes Equations ◽  
Physical Region ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Flow Modeling ◽  
Incompressible Fluid Flow ◽  
Navier Stokes Equations ◽  
Curvilinear Coordinate ◽  
Fluid Flow Modeling

Abstract A numerical algorithm for solving the Navier-Stokes equations for incom- pressible viscous fluid in an arbitrary two-dimensional region on nonstaggered grids is presented. The idea of the transition to a general curvilinear coordinate system, trans- forming the physical region into a parametrical square is used. For the discrete solution an unconditional a priory estimate has been obtained. The results of the benchmark computations for a driven skewed cavity flow and the results of the fluid flow modeling in a cavity of an arbitrary shape are given.

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