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Start Over Subject Navier-Stokes equation

1. A geometric improvement of the velocity-pressure local regularity criterion for a suitable weak solution to the Navier-Stokes equations

Creator:
Neustupa, Jiří
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Navier-Stokes equation, suitable weak solution, and regularity
Language:
English
Description:
We deal with a suitable weak solution (v, p) to the Navier-Stokes equations in a domain Ω ⊂ R 3 . We refine the criterion for the local regularity of this solution at the point (fx0, t0), which uses the L 3 -norm of v and the L 3/2 -norm of p in a shrinking backward parabolic neighbourhood of (x0, t0). The refinement consists in the fact that only the values of v, respectively p, in the exterior of a space-time paraboloid with vertex at (x0, t0), respectively in a ''small'' subset of this exterior, are considered. The consequence is that a singularity cannot appear at the point (x0, t0) if v and p are “smooth” outside the paraboloid.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. Numerical modelling of the velocity distribution in a compound channel

Creator:
Othman, F. and Valentine, E. M.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
compound channel, Navier-Stokes equation, non-linear k-ε turbulence model, reynolds stress model (RSM), velocityc distribution, secondary currents, zložený profil, rovnice Naviera-Stokesa, nelineárny k-ε model turbulencie, model Reynoldsových napätí (RSM), rozdelenie rýchlostí, and druhotné prúdy
Language:
Slovak
Description:
Uniform flow in compound channels has been studied in terms of a numerical model, called the NKE model. The model uses the three dimensional Navier-Stokes equations in conjunction with the non-linear k-ε turbulence model. The latter is used for the calculation of the Reynolds stress components responsible for the generation of the secondary currents. This model is based on the SIMPLE technique, and computes the six parameters U, V, W, P, k, and ε using wall functions on a Cartesian grid. The NKE model was used to simulate the compound open channel flows of the UK Flood Channel Facility run 080301 (Shiono and Knight, 1989). The Reynolds Stress Model (RSM) of FLUENT was also used as a comparison. The results obtained have shown that the NKE and RSM models can reasonably predict the primary mean velocity and secondary currents. Although agreement is certainly not perfect in every detail, the main features of the flow are reproduced. The bulging of the contours at the bottom corner of the main channel, the inclination of the contours near the free surface towards the channel centre, and the depression of the maximum velocity below the free surface can be seen. These are consistent with the pattern of the secondary flows, which are mainly formed by two vortices, namely the main channel vortex and flood plain vortex. These vortices, which originate near the main channel-flood plain junction, can be reproduced by the NKE and RSM models. and Štúdia pomocou numerického modelu NKF analyzuje ustálený rovnomerný prúd vody v koryte zloženom z kinety a dvoch symetrických beriem so zvislými stranami. Model využíva tri rovnice Naviera- Stokesa a nelineárny k-ε model turbulencie, ktorý simuluje Reynoldsove napätia, zodpovedné za druhotné prúdy. Tento model, založený na tzv. SIMPLE technike, počíta šesť parametrov U, V, W, P, k a ε pri použití stenových funkcií a karteziánskej siete. NKE model simuloval prúdenie, experimentálne pozorované na zariadení UK Flood Channel Facility ako séria č. 080301 (Shiono a Knight, 1989). Model pre Reynoldsove napätia (RSM) z balíka FLUENT bol tiež využitý na porovnanie. Výsledky ukázali, že modely NKE a RSM sú schopné predpovedať ako základné rýchlostné pole, tak aj vyvolané druhotné prúdenia. Aj keď zhoda s experimentom nie je v každom detaile úplná, hlavné znaky rýchlostného poľa sú zobrazené. Na simulácii možno vidieť zaoblenie rýchlostného poľa v rohoch dna hlavného kanála, sklon poľa v blízkosti hladiny smerom do stredu, ako aj pokles maxima rýchlosti pod voľnú hladinu. Tieto efekty sú v súlade s obrazom druhotných prúdov, ktoré sú tvorené hlavne dvoma vírmi - vírom kinety a vírom bermy. Tieto víry, vznikajúce pri spojení kinety s bermou, môžu byť reprodukované modelmi NKE a RSM.
Rights:
http://creativecommons.org/licenses/by-nc-sa/4.0/ and policy:public

3. Numerical simulation of transitional flows with laminar kinetic energy

Creator:
Fürst, Jiří
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
turbulence, transition, and Navier-Stokes equation
Language:
English
Description:
The article deals with the numerical solution of transitional flows. The single-point k-kL-ω model of [7] based on the use of a laminar kinetic energy transport equation is considered. The model doesn‘t require to evaluate integral boundary layer parameters (e.g. boundary layer thickness) and is therefore suitable for implementation into codes working with general unstructured meshes. The performance of the model has been tested for the case of flows over a flat plate with zero and non-zero pressure gradients. The results obtained with our implementation of the model are compared to the experimental data of ERCOFTAC. and Obsahuje seznam literatury
Rights:
http://creativecommons.org/licenses/by-nc-sa/4.0/ and policy:public