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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.
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177 citations
TL;DR: Systematic numerical experiments indicate that a second order implicit time discretization of the viscous term, with the pressure and convective terms treated explicitly, is stable under the standard CFL condition.
177 citations
TL;DR: In this paper, a 2D version of Moehring's equation is developed and used in conjunction with source terms computed in the simulation to predict the far-field sound from corotating vortices.
Abstract: The far-field sound from corotating vortices is computed by direct computation of the unsteady, compressible Navier-Stokes equations on a computational mesh that extends to two acoustic wavelengths in all directions. The vortices undergo a period of corotation followed by a sudden merger. A 2D version of Moehring's equation is developed and used in conjunction with source terms computed in the simulation to predict the far-field sound. The prediction agrees with the simulation to within 3 percent. Results of far-field pressure fluctuations for an acoustically noncompact case are also presented for which the prediction is 66 percent too high. Results also indicate that the monopole contribution of 'viscous sound' is negligible for this flow.
177 citations
TL;DR: It is shown that near the onset of this instability, traffic flow is described by a perturbed Korteweg--de Vries (KdV) equation, and the traffic jam can be identified with a soliton solution of the KdV equation.
Abstract: The flow of traffic on a long section of road without entrances or exits can be modeled by continuum equations similar to those describing fluid flow. In a certain range of traffic density, steady flow becomes unstable against the growth of a cluster, or ``phantom'' traffic jam, which moves at a slower speed than the otherwise homogeneous flow. We show that near the onset of this instability, traffic flow is described by a perturbed Korteweg--de Vries (KdV) equation. The traffic jam can be identified with a soliton solution of the KdV equation. The perturbation terms select a unique member of the continuous family of KdV solitons. These results may also apply to the dynamics of granular relaxation.
177 citations
Book•
01 Jan 1997
TL;DR: This chapter discusses quasi-Compressibility methods for projection schemes with structure from Euler to Revised Projection Schemes and time Discretization on Time-Grids.
Abstract: Introduction - Preliminareis - Stationary Quasi-Compressibility Methods: The Penalty Method and the Pressure Stabilization Method - Nonstationary Quasi-Compressibility Methods - Mixed Quasi-Compressibility Methods - The Projection Scheme of Chorin - The Projection Scheme of Van Kan - Two Modified Chorin Schemes - Multi-Component Schemes - Time Discretization on Time-Grids with Structure from Euler to Revised Projection Schemes
176 citations