Analytic solutions of the Navier-Stokes equations

2001 ◽  
Vol 50 (2) ◽  
pp. 299-311 ◽  
Author(s):  
Maria Carmela Lombardo
Keyword(s):  
Stokes Equations ◽  
Analytic Solutions ◽  
Navier Stokes ◽  
Navier Stokes Equations

scholarly journals ANALYTIC SOLUTIONS OF A TWO-FLUID HYDRODYNAMIC MODEL

2021 ◽  
Vol 26 (4) ◽  
pp. 582-590
Author(s):  
Imre Ferenc Barna ◽  
László Mátyás
Keyword(s):  
Stokes Equations ◽  
Analytic Solutions ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
One Dimensional ◽  
Two Fluids ◽  
Void Fractions ◽  
Self Similar ◽  
Cartesian Coordinate ◽  
Two Fluid

We investigate a one dimensional flow described with the non-compressible coupled Euler and non-compressible Navier-Stokes equations in the Cartesian coordinate system. We couple the two fluids through the continuity equation where different void fractions can be considered. The well-known self-similar Ansatz was applied and analytic solutions were derived for both velocity and pressure field as well.

scholarly journals Investigation of the Onset of Turbulence in Boundary Layers and the Implications for Solutions of the Navier-Stokes Equations.

2020 ◽  
Author(s):  
Andrew Logan
Keyword(s):  
Boundary Layer ◽  
Fluid Flow ◽  
Flat Plate ◽  
Stokes Equations ◽  
Analytic Solutions ◽  
Navier Stokes ◽  
Pressure Gradients ◽  
Navier Stokes Equations ◽  
Viscous Fluid Flow ◽  
Onset Of Turbulence

This paper investigates the onset of turbulence in incompressible viscous fluid flow over a flat plate by looking at the pressure gradients implied by the Blasius solution for laminar fluid flow and adjusting the predicted flow, leading to a mathematically predictable flow separation in the boundary layer and the onset of turbulence (including both transition and fully turbulent regions - both with and without the presence of a flat plate). It then considers the implications for potential analytic solutions to the Navier-Stokes Equations of the fact that it is possible to predict turbulence and a singularity for many flows (at any velocity).

Lattice Boltzmann Model for Incompressible Axisymmetric Thermal Flows With Swirl

2018 ◽  
Author(s):  
Insaf Mehrez ◽  
Ramla Gheith ◽  
Fethi Aloui ◽  
Samia Ben Nasrallah
Keyword(s):  
Lattice Boltzmann ◽  
Stokes Equations ◽  
Thermal Conditions ◽  
Analytic Solutions ◽  
Lattice Boltzmann Model ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Wall Boundary Conditions ◽  
Physical Phenomena ◽  
Thermal Flows

This paper presents a Lattice Boltzmann (LB) model for incompressible axisymmetric thermal flows. The forces and source terms are added into the Lattice Boltzmann Equation (LBE) and the incompressible Navier-Stokes equations are recovered by the Chapman-Enskog expansion. The model of Zhou [1] is applied for axial, radial and azimuthal velocities and the model of Q.Li et al [2] is computed for temperature variation. The source term of the scheme is simple and without velocity gradient terms. This approach can solve problems including several physical phenomena and complicated force forms as the flow between two coaxial cylinders. Good agreement is obtained between the present work, the analytic solutions and results of previous studies in cylindrical pipe. It proves the efficiency and simplicity of the proposed model compared to other ones. The Taylor-Couette (TC) system is treated with water flow characterized by a radius ratio η = 0.5 and an aspect ratio Γ = 3.8. Three Reynolds numbers of 85, 100 and 150 are tested. The influence of the end-wall boundary conditions and the influence of thermal conditions on the flow structure and on the temperature distribution along the inner and outer cylinders are analyzed.

Uniform analytic solutions for fractional Navier–Stokes equations

2021 ◽  
Vol 112 ◽  
pp. 106784
Author(s):  
Zhenzhen Lou ◽  
Qixiang Yang ◽  
Jianxun He ◽  
Kaili He
Keyword(s):  
Stokes Equations ◽  
Analytic Solutions ◽  
Navier Stokes ◽  
Navier Stokes Equations

On the unsteady squeezing of a viscous fluid from a tube

1979 ◽  
Vol 21 (1) ◽  
pp. 65-74 ◽  
Author(s):  
F. M. Skalak ◽  
C. Y. Wang
Keyword(s):  
Viscous Fluid ◽  
Numerical Scheme ◽  
Stokes Equations ◽  
Analytic Solutions ◽  
Linear Ordinary Differential Equation ◽  
Navier Stokes ◽  
Relative Importance ◽  
Dimensional Parameter ◽  
Navier Stokes Equations ◽  
Flow Reversals

AbstractViscous fluid is squeezed out from a shrinking (or expanding) tube whose radius varies with time as (1 – βt)½. The full Navier–Stokes equations reduce to a non-linear ordinary differential equation governed by a non-dimensional parameter S representing the relative importance of unsteadiness to viscosity. This paper studies the analytic solutions for large | S | through the method of matched asymptotic expansions. A simple numerical scheme for integration is presented. It is found that boundary layers exist near the walls for large | S |. In addition, flow reversals and oscillations of the velocity profile occur for large negative S (fast expansion of the tube).

scholarly journals Generator functions and their applications

2021 ◽  
Vol 8 (20) ◽  
pp. 245-251
Author(s):  
Emmanuel Grenier ◽  
Toan Nguyen
Keyword(s):  
Evolution Equations ◽  
Stokes Equations ◽  
Short Note ◽  
Analytic Solutions ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Japan Acad ◽  
Appl Math ◽  
Classical Evolution ◽  
Short Presentation

We had introduced so called generators functions to precisely follow the regularity of analytic solutions of Navier-Stokes equations earlier (see Grenier and Nguyen [Ann. PDE 5 (2019)]. In this short note, we give a short presentation of these generator functions and use them to construct analytic solutions to classical evolution equations, which provides an alternative way to the use of the classical abstract Cauchy-Kovalevskaya theorem (see Asano [Proc. Japan Acad. Ser. A Math. Sci. 64 (1988), pp. 102–105], Baouendi and Goulaouic [Comm. Partial Differential Equations 2 (1977), pp. 1151–1162], Caflisch [Bull. Amer. Math. Soc. (N.S.) 23 (1990), pp. 495–500], Nirenberg [J. Differential Geom. 6 (1972), pp. 561–576], Safonov [Comm. Pure Appl. Math. 48 (1995), pp. 629–637]).

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