Navier-Stokes Research Papers - Academia.edu (original) (raw)

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In this paper we write, analyze and experimentally compare three different numerical schemes dedicated to the one dimensional barotropic Navier-Stokes equations: • a staggered scheme based on the Rusanov one for the inviscid (Euler)... more

In this paper we write, analyze and experimentally compare three different numerical schemes dedicated to the one dimensional barotropic Navier-Stokes equations: • a staggered scheme based on the Rusanov one for the inviscid (Euler) system, • a staggered pseudo-Lagrangian scheme in which the mesh "follows" the fluid, • the Eulerian projection (on a fixed mesh) of the preceding scheme. All these schemes only involve the resolution of linear systems (all the nonlinear terms are solved in an explicit way). We propose numerical illustrations of their behaviors on particular solutions in which the density has discontinuities (hereafter called Hoff solutions). We show that the three schemes seem to converge to the same solutions, and we compare the evolution of the amplitude of the discontinuity of the numerical solution (with the pseudo-Lagrangian scheme) with the one predicted by Hoff and observe a good agreement.

• • by ATSOU kevin and +1
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  • Compressible Fluid Dynamics, Navier-Stokes, Mathematical Aspects of Navier Stoke's Equations
• • by Marco Cannone
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  • Navier-Stokes Equations, Navier Stokes, Equações de Navier-Stokes (Navier-Stokes Equations), Equações de Navier-Stokes
• • by HAMID mo
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  • Finite differences, Implicit, Navier-Stokes, Curvilinear Coordinates

Physics paper by Australia's Dr Peter Donald Rodgers

• • by Peter Rodgers
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  • Mathematics, Physics, Theoretical Physics, Quantum Physics

Physics paper by Australia's Dr Peter Donald Rodgers

• • by Peter Rodgers
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  • Mathematics, Physics, Theoretical Physics, Quantum Physics

Physics paper by Australia's Dr Peter Donald Rodgers

• • by Peter Rodgers
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  • Mathematics, Physics, Mathematics Education, Physics Education

A 3-D description of a flow past a short cyllinder shows that there is no paradox in this flow. The paradox appears only when a 2-D simplification is used.

• • by Mário Barbosa Villas Boas
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  • Partial Differential Equations, Computational Fluid Dynamics, Computational Fluid Mechanics, Fluid Dynamics
• • by Marco Cannone
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  • Navier-Stokes Equations, Navier Stokes, Equações de Navier-Stokes, Navier-Stokes
• • by Marco Cannone
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  • Navier-Stokes Equations, Navier Stokes, Equações de Navier-Stokes (Navier-Stokes Equations), Equações de Navier-Stokes
• • by Marco Cannone
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  • Navier-Stokes Equations, Navier Stokes, Equações de Navier-Stokes (Navier-Stokes Equations), Equações de Navier-Stokes

Physics paper by Australia's Dr Peter Donald Rodgers

• • by Peter Rodgers
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  • Mathematics, Physics, Theoretical Physics, Mathematics Education
• • by Marco Cannone
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  • Navier-Stokes Equations, Navier Stokes, Equações de Navier-Stokes (Navier-Stokes Equations), Equações de Navier-Stokes
• • by Marco Cannone
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  • Navier-Stokes Equations, Boltzmann Transport Equation, Equações de Navier-Stokes, Navier-Stokes
• • by Marco Cannone
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  • Navier-Stokes Equations, Navier Stokes, Navier-Stokes, Mathematical Aspects of Navier Stoke's Equations

As continuation of method described in part 1, this paper describes how to handle with the convective terms using the method proposed in part 1

• • by Mário Barbosa Villas Boas
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  • Partial Differential Equations, Computational Fluid Dynamics, Fluid Mechanics, Computational Fluid Mechanics

This paper describes a method for direct numerical solution of Navier Stokes Equation.

• • by Mário Barbosa Villas Boas
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  • Partial Differential Equations, Computational Fluid Dynamics, Fluid Mechanics, Computational Fluid Mechanics
• • by Marco Cannone
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  • Navier-Stokes Equations, Navier Stokes, Equações de Navier-Stokes (Navier-Stokes Equations), Equações de Navier-Stokes
• • by Marco Cannone
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  • Navier-Stokes Equations, Navier Stokes, Equações de Navier-Stokes (Navier-Stokes Equations), Equações de Navier-Stokes
• • by Marco Cannone
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  • Navier-Stokes Equations, Navier Stokes, Equações de Navier-Stokes, Navier-Stokes
• • by Marco Cannone
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  • Navier-Stokes Equations, Navier Stokes, Equações de Navier-Stokes (Navier-Stokes Equations), Equações de Navier-Stokes
• • by Marco Cannone
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  • Navier-Stokes Equations, Equações de Navier-Stokes (Navier-Stokes Equations), Equações de Navier-Stokes, Navier-Stokes

Applications of understanding are extracted from the Clay Mathematics Institute's paper on the Navier-Stokes equations which seeks to find a force, pressure, and initial conditions in an infinitely differentiable non-divergent vector... more

Applications of understanding are extracted from the Clay Mathematics Institute's paper on the Navier-Stokes equations which seeks to find a force, pressure, and initial conditions in an infinitely differentiable non-divergent vector space of an imcompressible fluid. A proof for equation (9) of that paper is produced.

• • by Michael T Chase
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  • Navier-Stokes Equations, Navier Stokes, Navier-Stokes, Navier-Stokes Solutions
• • by Marco Cannone
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  • Navier-Stokes Equations, Navier Stokes, Equações de Navier-Stokes, Navier-Stokes
• • by Marco Cannone
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  • Navier-Stokes Equations, Navier Stokes, Navier-Stokes, Mathematical Aspects of Navier Stoke's Equations
• • by Marco Cannone
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  • Navier-Stokes Equations, Navier Stokes, Equações de Navier-Stokes (Navier-Stokes Equations), Equações de Navier-Stokes
• • by Marco Cannone
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  • Navier-Stokes Equations, Navier Stokes, Navier-Stokes, Mathematical Aspects of Navier Stoke's Equations
• • by Marco Cannone
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  • Navier-Stokes Equations, Navier Stokes, Equações de Navier-Stokes (Navier-Stokes Equations), Equações de Navier-Stokes

Mathematical simulation of an external 3-D flow past a short solid cylinder show some astonishing behaviour. The author invite researcher to verify the existence of such fenomena and, if found true, to review all that have been stated for... more

Mathematical simulation of an external 3-D flow past a short solid cylinder show some astonishing behaviour. The author invite researcher to verify the existence of such fenomena and, if found true, to review all that have been stated for 2-D flows.

• • by Mário Barbosa Villas Boas
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  • Computational Fluid Dynamics, Fluid Mechanics, Computational Fluid Mechanics, Fluid Dynamics

Stokes proposed a very ingenious method for describing 2-D flows, which uses one single equation that represents 3 different ones. However, this method is completelly useless to describe 3-D flows. Those have been a challenge to... more

Stokes proposed a very ingenious method for describing 2-D flows, which uses one single equation that represents 3 different ones. However, this method is completelly useless to describe 3-D flows. Those have been a challenge to mechanical engineers. So far there is no method described in the literature that allows analytical solution to 3-D flows. Numerical methods use routines that are extremely expensive, in terms of computer resources. This article proposes a method that allows analytical solution to 3-D flows - if the convective terms are not present - and present some advatages for using in numerical simulators. Because it is too long, it has been divided into parts. This is part one, an introduction and the description of its use only in the simplest situation of all: no convective terms and recttangular coordinates.

• • by Mário Barbosa Villas Boas
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  • Partial Differential Equations, Computational Fluid Dynamics, Finite Element Methods, Fluid Mechanics
• • by Marco Cannone
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  • Navier-Stokes Equations, Navier Stokes, Equações de Navier-Stokes (Navier-Stokes Equations), Equações de Navier-Stokes

In parts 1 and 2 it has been shown how to use this method when the convective terms are not present. In those cases, if the boundaries are not much irregular, analytical solutions are possible. In this article it is shown how to use it... more

In parts 1 and 2 it has been shown how to use this method when the convective terms are not present. In those cases, if the boundaries are not much irregular, analytical solutions are possible. In this article it is shown how to use it when the convective terms ARE present. In those cases, only numerical methods can be applied to solve the equations. No example of numerical aplication of the method is presented.

• • by Mário Barbosa Villas Boas
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  • Partial Differential Equations, Computational Fluid Dynamics, Finite Element Methods, Fluid Mechanics

We use a method based on the lubrication approximation in conjunction with a residual-based mass-continuity iterative solution scheme to compute the flow rate and pressure field in distensible converging-diverging tubes for Navier-Stokes... more

We use a method based on the lubrication approximation in conjunction with a residual-based mass-continuity iterative solution scheme to compute the flow rate and pressure field in distensible converging-diverging tubes for Navier-Stokes fluids. We employ an analytical formula derived from a one-dimensional version of the Navier-Stokes equations to describe the underlying flow model that provides the residual function. This formula correlates the flow rate to the boundary pressures in straight cylindrical elastic tubes with constant-radius. We validate our findings by the convergence toward a final solution with fine discretization as well as by comparison to the Poiseuille-type flow in its convergence toward analytic solutions found earlier in rigid converging-diverging tubes. We also tested the method on limiting special cases of cylindrical elastic tubes with constant-radius where the numerical solutions converged to the expected analytical solutions. The distensible model has also been endorsed by its convergence toward the rigid Poiseuille-type model with increasing the tube wall stiffness. Lubrication-based one-dimensional finite element method was also used for verification. In this investigation five converging-diverging geometries are used for demonstration, validation and as prototypes for modeling converging-diverging geometries in general.

• • by Taha Sochi
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  • Computational Fluid Dynamics, Fluid Mechanics, Computational Fluid Mechanics, Fluid structure interaction
• • by Marco Cannone
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  • Navier-Stokes Equations, Navier-Stokes, Mathematical Aspects of Navier Stoke's Equations, Heat Equation

Let’s put ourselves on a boat and watch waves travel behind it. The same concept can apply to air flow when traveling on an air plane. Previously and currently, mathematicians believe the wave mechanics and air flow is explained through a... more

Let’s put ourselves on a boat and watch waves travel behind it. The same concept can apply to air flow when traveling on an air plane. Previously and currently, mathematicians believe the wave mechanics and air flow is explained through a thorough understanding of existing solutions to Navier-Stokes equations. Since the nineteenth century, the understanding of these equations are unsubstantial. The goal is to create substantial qualitative input towards generating a mathematical theory unlocking implicit information within the Navier-Stokes equations. The literature will contain mathematical physical methods for locating closed general solutions applied to various fields.

• • by Tim Tarver
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  • Mathematics, Ordinary Differential Equations, Partial Differential Equations, Mathematics Education
• • by Marco Cannone
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  • Navier-Stokes Equations, Navier Stokes, Equações de Navier-Stokes (Navier-Stokes Equations), Equações de Navier-Stokes
• • by Marco Cannone
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  • Navier-Stokes Equations, Navier Stokes, Equações de Navier-Stokes (Navier-Stokes Equations), Equações de Navier-Stokes
• • by Marco Cannone
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  • Navier-Stokes Equations, Navier Stokes, Equações de Navier-Stokes (Navier-Stokes Equations), Equações de Navier-Stokes

For completness of the workd here shown, this Excel datasheet shows the results of the analytic and numeric solution as streamlines in order to validate both

• • by Mário Barbosa Villas Boas
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  • Partial Differential Equations, Numerical Simulations, Computational Fluid Dynamics, Fluid Mechanics

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