Euler and Navier—Stokes Equations for Incompressible Fluids

2010 ◽  
pp. 531-614
Author(s):  
Michael E. Taylor
Keyword(s):  
Stokes Equations ◽  
Incompressible Fluids ◽  
Navier Stokes ◽  
Navier Stokes Equations

scholarly journals Well-posedness of 2-D and 3-D swimming models in incompressible fluids governed by Navier–Stokes equations

2015 ◽  
Vol 429 (2) ◽  
pp. 1059-1085 ◽  
Author(s):  
Alexander Khapalov ◽  
Piermarco Cannarsa ◽  
Fabio S. Priuli ◽  
Giuseppe Floridia
Keyword(s):  
Stokes Equations ◽  
Incompressible Fluids ◽  
Navier Stokes ◽  
Well Posedness ◽  
Navier Stokes Equations

scholarly journals A class of exact solutions of equations for plane steady motion of incompressible fluids of variable viscosity in presence of body force

2018 ◽  
Vol 7 (3) ◽  
pp. 77
Author(s):  
Mushtaq Ahmed ◽  
Waseem Ahmed Khan ◽  
S M. Shad Ahsen
Keyword(s):  
Exact Solutions ◽  
Body Force ◽  
Stokes Equations ◽  
Variable Viscosity ◽  
Steady Motion ◽  
Incompressible Fluids ◽  
Polar Coordinates ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
First Case

This paper determines a class of exact solutions for plane steady motion of incompressible fluids of variable viscosity with body force term in the Navier-Stokes equations. The class consists of stream function  characterized by equation , in polar coordinates ,  where ,  and  are continuously differentiable functions, derivative of  is non-zero but double derivative of  is zero. We find exact solutions, for a suitable component of body force, considering two cases based on velocity profile. The first case fixes both the functions ,  and provides viscosity as function of temperature. Where as the second case fixes the function , leaves  arbitrary and provides viscosity and temperature for the arbitrary function . In both the cases, we can create infinite set of expressions for streamlines, viscosity function, generalized energy function and temperature distribution in the presence of body force.  

scholarly journals Using Fractal Calculus to Solve Fractal Navier–Stokes Equations, and Simulation of Laminar Static Mixing in COMSOL Multiphysics

2021 ◽  
Vol 5 (1) ◽  
pp. 16
Author(s):  
Amir Pishkoo ◽  
Maslina Darus
Keyword(s):  
Laminar Flow ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Incompressible Fluids ◽  
Navier Stokes ◽  
Fractal Structures ◽  
Navier Stokes Equations ◽  
Static Mixers ◽  
Two Fluids ◽  
Physical Conditions

Navier–Stokes equations describe the laminar flow of incompressible fluids. In most cases, one prefers to solve either these equations numerically, or the physical conditions of solving the problem are considered more straightforward than the real situation. In this paper, the Navier–Stokes equations are solved analytically and numerically for specific physical conditions. Using Fα-calculus, the fractal form of Navier–Stokes equations, which describes the laminar flow of incompressible fluids, has been solved analytically for two groups of general solutions. In the analytical section, for just “the single-phase fluid” analytical answers are obtained in a two-dimensional situation. However, in the numerical part, we simulate two fluids’ flow (liquid–liquid) in a three-dimensional case through several fractal structures and the sides of several fractal structures. Static mixers can be used to mix two fluids. These static mixers can be fractal in shape. The Sierpinski triangle, the Sierpinski carpet, and the circular fractal pattern have the static mixer’s role in our simulations. We apply these structures just in zero, first and second iterations. Using the COMSOL software, these equations for “fractal mixing” were solved numerically. For this purpose, fractal structures act as a barrier, and one can handle different types of their corresponding simulations. In COMSOL software, after the execution, we verify the defining model. We may present speed, pressure, and concentration distributions before and after passing fluids through or out of the fractal structure. The parameter for analyzing the quality of fractal mixing is the Coefficient of Variation (CoV).

A quasi-incompressible diffuse interface model with phase transition

2014 ◽  
Vol 24 (05) ◽  
pp. 827-861 ◽  
Author(s):  
Gonca L. Aki ◽  
Wolfgang Dreyer ◽  
Jan Giesselmann ◽  
Christiane Kraus
Keyword(s):  
Stokes Equations ◽  
Incompressible Fluids ◽  
The Other ◽  
Diffuse Interface ◽  
Navier Stokes ◽  
Interface Model ◽  
Diffuse Interface Model ◽  
Navier Stokes Equations ◽  
Interfacial Conditions ◽  
Two Component

This work introduces a new thermodynamically consistent diffuse model for two-component flows of incompressible fluids. For the introduced diffuse interface model, we investigate physically admissible sharp interface limits by matched asymptotic techniques. To this end, we consider two scaling regimes where in one case we recover the Euler equations and in the other case the Navier–Stokes equations in the bulk phases equipped with admissible interfacial conditions. For the Navier–Stokes regime, we further assume the densities of the fluids are close to each other in the sense of a small parameter which is related to the interfacial thickness of the diffuse model.

ON THE NON-NEWTONIAN INCOMPRESSIBLE FLUIDS

1993 ◽  
Vol 03 (01) ◽  
pp. 35-63 ◽  
Author(s):  
JOSEF MÁLEK ◽  
JINDŘICH NEČAS ◽  
MICHAEL RŮŽIČKA
Keyword(s):  
Weak Solution ◽  
Stress Tensor ◽  
Growth Condition ◽  
Stokes Equations ◽  
Periodic Problem ◽  
Incompressible Fluids ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Nonlinear Stress ◽  
Special Case

The Navier-Stokes equations can be included as a special case into the class of non-Newtonian incompressible fluids with the nonlinear stress tensor τ=τ(e), the components of which satisfy the p-growth condition. Measure-valued solutions already exist for p>2n/(n+2). For the space periodic problem, the existence of the weak solution is then obtained for p>3n/(n+2). These solutions are regular and unique for p≥1+2n/(n+2).

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