scholarly journals A multilevel method of nonlinear Galerkin type for the Navier-Stokes equations

2005 ◽  
Vol 2005 (3) ◽  
pp. 341-363
Author(s):  
Said El Hajji ◽  
Khalid Ilias
Keyword(s):  
Fourier Series ◽  
Major Part ◽  
Stokes Equations ◽  
The Other ◽  
Navier Stokes ◽  
Multilevel Method ◽  
Navier Stokes Equations ◽  
Relative Information ◽  
Nonlinear Galerkin Method ◽  
Simplified Calculation

The basic idea of this new method resides in the fact that the major part of the relative information to the solution to calculate is contained in the small modes of a development of Fourier series; the raised modes of which the coefficients associated being small, being negligible to every instant, however, the effect of these modes on a long interval of time is not negligible. The nonlinear Galerkin method proposes economical treatment of these modes that permits, in spite of a simplified calculation, taking into account their interaction correctly with the other modes. After the introduction of this method, we elaborate an efficient strategy for its implementation.

scholarly journals Mixing of Particles in Micromixers under Different Angles and Velocities of the Incoming Water

Proceedings ◽  
2018 ◽  
Vol 2 (11) ◽  
pp. 577 ◽  
Author(s):  
Evangelos Karvelas ◽  
Christos Liosis ◽  
Theodoros Karakasidis ◽  
Ioannis Sarris
Keyword(s):  
Stokes Equations ◽  
Velocity Ratio ◽  
The Other ◽  
Navier Stokes ◽  
Contaminated Water ◽  
Solution Flow ◽  
Navier Stokes Equations ◽  
Inlet Velocity ◽  
Metal Capture ◽  
Discrete Motion

A possible solution for water purification from heavy metals is to capture them by using nanoparticles in microfluidic ducts. In this technique, heavy metal capture is achieved by effectively mixing two streams, a nanoparticle solution and the contaminated water. In the present work, particles and water mixing is numerically studied for various inlet velocity ratios and inflow angles of the two streams. The Navier-Stokes equations are solved for the water flow while the discrete motion of particles is evaluated by a Lagrangian method. Results showed that as the velocity ratio between the inlet streams increases, by increasing the particles solution flow, the mixing of particles with the contaminated water is increased. Thus, nanoparticles are more uniformly distributed in the duct. On the other hand, angle increase between the inflow streams ducts is found to be less significant.

scholarly journals Effects of Hydrostatic Pocket Shape on the Flow Pattern and Pressure Distribution

1995 ◽  
Vol 1 (3-4) ◽  
pp. 225-235 ◽  
Author(s):  
M. J. Braun ◽  
M. Dzodzo
Keyword(s):  
Numerical Simulation ◽  
Pressure Distribution ◽  
Flow Pattern ◽  
Stokes Equations ◽  
The Other ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Hydrostatic Bearing ◽  
Collocated Grid ◽  
Dimensionless Formulation

The flow in a hydrostatic pocket is numerically simulated using a dimensionless formulation of the 2-D Navier-Stokes equations written in primitive variables, for a body fitted coordinates system, and applied through a collocated grid. In essence, we continue the work of Braun et al. 1993a, 1993b] and extend it to the study of the effects of the pocket geometric format on the flow pattern and pressure distribution. The model includes the coupling between the pocket flow and a finite length feedline flow, on one hand, and the pocket and its adjacent lands on the other hand. In this context we shall present, on a comparative basis, the flow and the pressure patterns at the runner surface for square, ramped-Rayleigh step, and arc of circle pockets. Geometrically all pockets have the same footprint, same lands length, and same capillary feedline. The numerical simulation uses the Reynolds number based on the lid(runner) velocity and the inlet jet strengthFas the dynamic similarity parameters. The study aims at establishing criteria for the optimization of the pocket geometry in the larger context of the performance of a hydrostatic bearing.

scholarly journals Investigating the Effect of the Closure in Partially-Averaged Navier–Stokes Equations

2019 ◽  
Vol 141 (12) ◽  
Author(s):  
Filipe S. Pereira ◽  
Luís Eça ◽  
Guilherme Vaz
Keyword(s):  
Reynolds Number ◽  
Shear Stress ◽  
Coherent Structures ◽  
Stokes Equations ◽  
The Other ◽  
Navier Stokes ◽  
Governing Equations ◽  
Navier Stokes Equations ◽  
Auxiliary Functions ◽  
Modeling Accuracy

The importance of the turbulence closure to the modeling accuracy of the partially-averaged Navier–Stokes equations (PANS) is investigated in prediction of the flow around a circular cylinder at Reynolds number of 3900. A series of PANS calculations at various degrees of physical resolution is conducted using three Reynolds-averaged Navier–Stokes equations (RANS)-based closures: the standard, shear-stress transport (SST), and turbulent/nonturbulent (TNT) k–ω models. The latter is proposed in this work. The results illustrate the dependence of PANS on the closure. At coarse physical resolutions, a narrower range of scales is resolved so that the influence of the closure on the simulations accuracy increases significantly. Among all closures, PANS–TNT achieves the lowest comparison errors. The reduced sensitivity of this closure to freestream turbulence quantities and the absence of auxiliary functions from its governing equations are certainly contributing to this result. It is demonstrated that the use of partial turbulence quantities in such auxiliary functions calibrated for total turbulent (RANS) quantities affects their behavior. On the other hand, the successive increase of physical resolution reduces the relevance of the closure, causing the convergence of the three models toward the same solution. This outcome is achieved once the physical resolution and closure guarantee the precise replication of the spatial development of the key coherent structures of the flow.

A note on viscous flow induced by half-line sources bounded by conical surfaces

2019 ◽  
Author(s):  
Prabakaran Rajamanickam ◽  
Adam D Weiss
Keyword(s):  
Radial Velocity ◽  
Line Source ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
The Other ◽  
Half Line ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Axisymmetric Solutions ◽  
Conical Surfaces

Summary In this article, axisymmetric solutions of the Navier–Stokes equations governing the flow induced by a half-line source when the fluid domain is bounded by a conical wall are discussed. Two types of boundary conditions are identified; one in which the radial velocity along the axis is prescribed, and the other in which the radial velocity along the axis is obtained as an eigenvalue of the problem. The existence of these solutions is limited to a range of Reynolds numbers, and the transition from one case to the other is discussed in detail.

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