scholarly journals Properties of time-dependent statistical solutions of the three-dimensional Navier-Stokes equations

2013 ◽  
Vol 63 (6) ◽  
pp. 2515-2573 ◽  
Author(s):  
Ciprian Foias ◽  
Ricardo M. S. Rosa ◽  
Roger Temam
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Time Dependent ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Statistical Solutions

scholarly journals A Code for Simulating Heat Transfer in Turbulent Channel Flow

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 756
Author(s):  
Federico Lluesma-Rodríguez ◽  
Francisco Álcantara-Ávila ◽  
María Jezabel Pérez-Quiles ◽  
Sergio Hoyas
Keyword(s):  
Heat Transfer ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Turbulent Channel Flow ◽  
Passive Scalar ◽  
Direct Numerical Simulations ◽  
Time Dependent ◽  
Navier Stokes ◽  
Thermal Flow ◽  
Navier Stokes Equations

One numerical method was designed to solve the time-dependent, three-dimensional, incompressible Navier–Stokes equations in turbulent thermal channel flows. Its originality lies in the use of several well-known methods to discretize the problem and its parallel nature. Vorticy-Laplacian of velocity formulation has been used, so pressure has been removed from the system. Heat is modeled as a passive scalar. Any other quantity modeled as passive scalar can be very easily studied, including several of them at the same time. These methods have been successfully used for extensive direct numerical simulations of passive thermal flow for several boundary conditions.

Stretching effects on the three-dimensional stability of vortices with axial flow

2002 ◽  
Vol 454 ◽  
pp. 419-442 ◽  
Author(s):  
IVAN DELBENDE ◽  
MAURICE ROSSI ◽  
STÉPHANE LE DIZÈS
Keyword(s):  
Dimensional Stability ◽  
Strain Field ◽  
Stokes Equations ◽  
Linear Equations ◽  
Three Dimensional ◽  
Axial Flow ◽  
Time Dependent ◽  
Navier Stokes ◽  
Simultaneous Action ◽  
Navier Stokes Equations

The effect of stretching on the three-dimensional stability of a viscous unsteady vortex is addressed. The basic flow, which satisfies the Navier–Stokes equations, is a vortex with axial flow subjected to a time-dependent strain field oriented along its axis. The linear equations for the three-dimensional perturbations of the stretched vortex are first reduced by using successive changes of variables to equations which are almost identical to those of the unstretched vortex but with time-dependent parameters. These equations are then numerically solved in the particular case of the Batchelor vortex with a strain field which first compresses then stretches the vortex. Through this simulation, it is qualitatively demonstrated how the simultaneous action of stretching and azimuthal vorticity may destabilize a vortex. It is also argued that it provides a possible mechanism for the vortex bursts observed in turbulence experiments.

Numerical Simulations of Three-Dimensional Flows in a Cubic Cavity With an Oscillating Lid

1993 ◽  
Vol 115 (4) ◽  
pp. 680-686 ◽  
Author(s):  
Reima Iwatsu ◽  
Jae Min Hyun ◽  
Kunio Kuwahara
Keyword(s):  
Numerical Solutions ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Flow Characteristics ◽  
Time Dependent ◽  
Navier Stokes ◽  
Physical Parameters ◽  
Navier Stokes Equations ◽  
Sinusoidal Oscillations ◽  
Dependent Flow

Numerical studies are made of three-dimensional flow of a viscous fluid in a cubical container. The flow is driven by the top sliding wall, which executes sinusoidal oscillations. Numerical solutions are acquired by solving the time-dependent, three-dimensional incompressible Navier-Stokes equations by employing very fine meshes. Results are presented for wide ranges of two principal physical parameters, i.e., the Reynolds number, Re ≤ 2000 and the frequency parameter of the lid oscillation, ω′ ≤ 10.0. Comprehensive details of the flow structure are analyzed. Attention is focused on the three-dimensionality of the flow field. Extensive numerical flow visualizations have been performed. These yield sequential plots of the main flows as well as the secondary flow patterns. It is found that the previous two-dimensional computational results are adequate in describing the main flow characteristics in the bulk of interior when ω′ is reasonably high. For the cases of high-Re flows, however, the three-dimensional motions exhibit additional complexities especially when ω′ is low. It is asserted that, thanks to the recent development of the supercomputers, calculation of three-dimensional, time-dependent flow problems appears to be feasible at least over limited ranges of Re.

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