Numerical simulations using conserved wave absorption applied to Navier–Stokes equation model

Modeling statistical properties of motion of a Lagrangian particle advected by a high-Reynolds-number flow is of much practical interest and complement traditional studies of turbulence made in Eulerian framework. The strong and nonlocal character of Lagrangian particle coupling due to pressure effects makes the main obstacle to derive turbulence statistics from the three-dimensional Navier–Stokes equation; motion of a single fluid-particle is strongly correlated to that of the other particles. Recent breakthrough Lagrangian experiments with high resolution of Kolmogorov scale have motivated growing interest to acceleration of a fluid particle. Experimental stationary statistics of Lagrangian acceleration conditioned on Lagrangian velocity reveals essential dependence of the acceleration variance upon the velocity. This is confirmed by direct numerical simulations. Lagrangian intermittency is considerably stronger than the Eulerian one. Statistics of Lagrangian acceleration depends on Reynolds number. In this review we present description of new simple models of Lagrangian acceleration that enable data analysis and some advance in phenomenological study of the Lagrangian single-particle dynamics. Simple Lagrangian stochastic modeling by Langevin-type dynamical equations is one the widely used tools. The models are aimed particularly to describe the observed highly non-Gaussian conditional and unconditional acceleration distributions. Stochastic one-dimensional toy models capture main features of the observed stationary statistics of acceleration. We review various models and focus in a more detail on the model which has some deductive support from the Navier–Stokes equation. Comparative analysis on the basis of the experimental data and direct numerical simulations is made.

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Navier-Stokes equation

Physics Subject Headings (PhySH) ◽

10.29172/a3ff37a7-c0a4-48a9-a32f-0dbc060c2746 ◽

2018 ◽

Keyword(s):

Stokes Equation ◽

Navier Stokes ◽

Navier Stokes Equation

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6 Navier–Stokes equation in 2D and 3D

Critical Parabolic-Type Problems ◽

10.1515/9783110599831-006 ◽

2020 ◽

pp. 141-158

Keyword(s):

Stokes Equation ◽

Navier Stokes ◽

Navier Stokes Equation ◽

2D And 3D

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Wavelet-distributed approximating functional method for solving the Navier-Stokes equation

Computer Physics Communications ◽

10.1016/s0010-4655(98)00113-1 ◽

1998 ◽

Vol 115 (1) ◽

pp. 18-24 ◽

Cited By ~ 22

Author(s):

G.W. Wei ◽

D.S. Zhang ◽

S.C. Althorpe ◽

D.J. Kouri ◽

D.K. Hoffman

Keyword(s):

Stokes Equation ◽

Functional Method ◽

Navier Stokes ◽

Navier Stokes Equation

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Generalized Navier–Stokes Equations and Dynamics of Plane Molecular Media

Symmetry ◽

10.3390/sym13020288 ◽

2021 ◽

Vol 13 (2) ◽

pp. 288

Author(s):

Alexei Kushner ◽

Valentin Lychagin

Keyword(s):

Carbon Dioxide ◽

Internal Structure ◽

Stokes Equation ◽

Hydrogen Cyanide ◽

Stokes Equations ◽

Navier Stokes ◽

Navier Stokes Equation ◽

Navier Stokes Equations

The first analysis of media with internal structure were done by the Cosserat brothers. Birkhoff noted that the classical Navier–Stokes equation does not fully describe the motion of water. In this article, we propose an approach to the dynamics of media formed by chiral, planar and rigid molecules and propose some kind of Navier–Stokes equations for their description. Examples of such media are water, ozone, carbon dioxide and hydrogen cyanide.

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