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Navier–Stokes equations

About: Navier–Stokes equations is a research topic. Over the lifetime, 18180 publications have been published within this topic receiving 552555 citations. The topic is also known as: Navier-Stokes equations.


Papers
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Journal ArticleDOI
TL;DR: In this article, the authors considered the non-stationary Navier-Stokes problem in the half space R n ≥ 2 + (n ≥ 2) with constant equilibria and showed that the leading part of the solution behaves like diffusion waves and the other one purely diffusively.
Abstract: Asymptotic behavior of solutions of the compressible Navier-Stokes equations on the half space R n +(n≥2) is considered around a given constant equilibrium. A solution formula for the linearized problem is derived, and L p estimates for solutions of the linearized problem are obtained for 2≤p≤∞. It is shown that, as in the case of the Cauchy problem, the leading part of the solution of the linearized problem is decomposed into two parts, one that behaves like diffusion waves and the other one purely diffusively. There, however, are some aspects different from the Cauchy problem, especially in considering spatial derivatives. It is also shown that the solution of the linearized problem approaches for large times the solution of the nonstationary Stokes problem in some L p spaces; and, as a result, a solution formula for the nonstationary Stokes problem is obtained. Large-time behavior of solutions of the nonlinear problem is then investigated in L p spaces for 2≤p≤∞ by applying the results on the linearized analysis and the weighted energy method. The results indicate that there may be some nonlinear interaction phenomena not appearing in the Cauchy problem.

140 citations

Book
20 Nov 2001
TL;DR: In this paper, the authors discuss the properties of Turbulence and chaos in the context of empirical algorithms and analytic theories and mathematical aspects, and develop developed and developed Turbulences.
Abstract: 1 Continua and Generalities About Their Equations.- 2 Empirical Algorithms.- 3 Analytical Theories and Mathematical Aspects.- 4 Incipient Turbulence and Chaos.- 5 Ordering Chaos.- 6 Developed Turbulence.- 7 Statistical Properties of Turbulence.- Name Index.- Citations Index.

140 citations

Journal ArticleDOI
TL;DR: A new method for physically based modeling and interactive-rate simulation of 3D fluids in computer graphics by solving the 2D Navier-Stokes equations using a computational fluid dynamics method.

139 citations

Journal ArticleDOI
TL;DR: In this paper, a special near-wall subgrid-scale (SGS) model based on wall-parallel filtering and wall-normal averaging of the streamwise momentum equation was developed, with an assumption of local inner scaling used to reduce the unsteady term.
Abstract: We report large-eddy simulation (LES) of turbulent channel flow. This LES neither resolves nor partially resolves the near-wall region. Instead, we develop a special near-wall subgrid-scale (SGS) model based on wall-parallel filtering and wall-normal averaging of the streamwise momentum equation, with an assumption of local inner scaling used to reduce the unsteady term. This gives an ordinary differential equation (ODE) for the wall shear stress at every wall location that is coupled with the LES. An extended form of the stretched-vortex SGS model, which incorporates the production of near-wall Reynolds shear stress due to the winding of streamwise momentum by near-wall attached SGS vortices, then provides a log relation for the streamwise velocity at the top boundary of the near-wall averaged domain. This allows calculation of an instantaneous slip velocity that is then used as a ‘virtual-wall’ boundary condition for the LES. A Karman-like constant is calculated dynamically as part of the LES. With this closure we perform LES of turbulent channel flow for Reynolds numbers Re_τ based on the friction velocity u_τ and the channel half-width δ in the range 2 × 10^3 to 2 × 10^7. Results, including SGS-extended longitudinal spectra, compare favourably with the direct numerical simulation (DNS) data of Hoyas & Jimenez (2006) at Re_τ = 2003 and maintain an O(1) grid dependence on Re_τ.

139 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023183
2022389
2021544
2020509
2019545
2018575