scholarly journals Erratum: Yan Guo. Boltzmann diffusive limit beyond the Navier-Stokes approximation,Communications on Pure and Applied Mathematics (2006) 59(5) 626-687

2006 ◽  
Vol 60 (2) ◽  
pp. 291-293 ◽  
Author(s):  
Yan Guo
Keyword(s):  
Applied Mathematics ◽  
Navier Stokes ◽  
Stokes Approximation ◽  
Diffusive Limit

A Step Toward the Elucidation of Quantitative Laws of Nature

2020 ◽  
Vol 13 ◽  
pp. 72-82
Author(s):  
Stephen Perry ◽  
Keyword(s):  
Boundary Layer ◽  
Stokes Equations ◽  
Applied Mathematics ◽  
Laws Of Nature ◽  
Navier Stokes ◽  
Natural Phenomena ◽  
Navier Stokes Equations ◽  
Fine Grain ◽  
The World ◽  
Layer Solution

When we mathematically model natural phenomena, there is an assumption concerning how the mathematics relates to the actual phenomenon in question. This assumption is that mathematics represents the world by “mapping on” to it. I argue that this assumption of mapping, or correspondence between mathematics and natural phenomena, breaks down when we ignore the fine grain of our physical concepts. I show that this is a source of trouble for the mapping account of applied mathematics, using the case of Prandtl’s Boundary Layer solution to the Navier-Stokes equations.

scholarly journals Energy decay of vortices in viscous fluids: an applied mathematics view

2012 ◽  
Vol 709 ◽  
pp. 593-609 ◽  
Author(s):  
Jan Nordström ◽  
Björn Lönn
Keyword(s):  
Numerical Solutions ◽  
Stokes Equations ◽  
Applied Mathematics ◽  
Energy Decay ◽  
Viscous Fluids ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
The Matrix ◽  
High Order Finite Difference ◽  
Dissipative Terms

AbstractThe energy decay of vortices in viscous fluids governed by the compressible Navier–Stokes equations is investigated. It is shown that the main reason for the slow decay is that zero eigenvalues exist in the matrix related to the dissipative terms. The theoretical analysis is purely mathematical and based on the energy method. To check the validity of the theoretical result in practice, numerical solutions to the Navier–Stokes equations are computed using a stable high-order finite difference method. The numerical computations corroborate the theoretical conclusion.

scholarly journals Compressible Navier–Stokes approximation to the Boltzmann equation

2014 ◽  
Vol 256 (11) ◽  
pp. 3770-3816 ◽  
Author(s):  
Shuangqian Liu ◽  
Tong Yang ◽  
Huijiang Zhao
Keyword(s):  
Boltzmann Equation ◽  
Navier Stokes ◽  
Stokes Approximation ◽  
The Boltzmann Equation

A BGK model for small Prandtl number in the Navier-Stokes approximation

1993 ◽  
Vol 71 (1-2) ◽  
pp. 191-207 ◽  
Author(s):  
Fran�ois Bouchut ◽  
Beno�t Perthame
Keyword(s):  
Prandtl Number ◽  
Navier Stokes ◽  
Bgk Model ◽  
Stokes Approximation

SOLVING BURGERS EQUATION BY A MESHLESS METHOD

2005 ◽  
Vol 19 (28n29) ◽  
pp. 1651-1654 ◽  
Author(s):  
B. J. SHI ◽  
D. W. SHU ◽  
S. J. SONG ◽  
Y. M. ZHANG
Keyword(s):  
Shock Wave ◽  
Burgers Equation ◽  
Applied Mathematics ◽  
Reynolds Numbers ◽  
Least Square ◽  
Navier Stokes ◽  
Large Reynolds Number ◽  
Navier Stokes Equation ◽  
Point Collocation ◽  
Shock Wave Formation

Burgers equation is a fundamental partial differential equation of second order to describe the integrated process of convection-diffusion in physics. It occurs in various areas of applied mathematics and physics, such as modeling of turbulence, boundary layer behavior, shock wave formation, and mass transport. The convective and diffusive terms in Navier-Stokes equation are included in Burgers equation while the pressure term is neglected. A least-square point collocation meshless formula is proposed to discretize the Burgers equation. To verify the present meshless approach, the distributions of velocity for Burgers equation under different Reynolds numbers are investigated. Numerical results show that the proposed approach presents a good simulation of shock wave for Burgers equation with large Reynolds number.

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