Global regularity for the 2D micropolar Rayleigh-Bénard problem with partial dissipation

2022 ◽  
pp. 107899
Author(s):  
Haifeng Shang ◽  
Mengyu Guo
Keyword(s):  
Global Regularity ◽  
Partial Dissipation ◽  
Bénard Problem ◽  
Benard Problem ◽  
Rayleigh Benard

Global regularity for the micropolar Rayleigh-Bénard problem with only velocity dissipation

2021 ◽  
pp. 1-30
Author(s):  
Lihua Deng ◽  
Haifeng Shang
Keyword(s):  
Global Regularity ◽  
Special Structure ◽  
Regularity Of Solutions ◽  
Energy Methods ◽  
Regularity Problem ◽  
Interpolation Inequalities ◽  
Fourier Frequency ◽  
Bénard Problem ◽  
Benard Problem ◽  
Rayleigh Benard

This paper is concerned with the global regularity problem on the micropolar Rayleigh-Bénard problem with only velocity dissipation in $\mathbb {R}^{d}$ with $d=2\ or\ 3$ . By fully exploiting the special structure of the system, introducing two combined quantities and using the technique of Littlewood-Paley decomposition, we establish the global regularity of solutions to this system in $\mathbb {R}^{2}$ . Moreover, we obtain the global regularity for fractional hyperviscosity case in $\mathbb {R}^{3}$ by employing various techniques including energy methods, the regularization of generalized heat operators on the Fourier frequency localized functions and logarithmic Sobolev interpolation inequalities.

Stabilization of the no-motion state in the Rayleigh–Bénard problem

1994 ◽  
Vol 447 (1931) ◽  
pp. 587-607 ◽  
Keyword(s):  
Fluid Layer ◽  
Critical Rayleigh Number ◽  
Control Flow ◽  
Feedback Controller ◽  
Linear Stability Theory ◽  
Motion State ◽  
Conduction State ◽  
Bénard Problem ◽  
Benard Problem ◽  
Rayleigh Benard

Using linear stability theory and numerical simulations, we demonstrate that the critical Rayleigh number for bifurcation from the no-motion (conduction) state to the motion state in the Rayleigh–Bénard problem of an infinite fluid layer heated from below and cooled from above can be significantly increased through the use of a feedback controller effectuating small perturbations in the boundary data. The controller consists of sensors which detect deviations in the fluid’s temperature from the motionless, conductive values and then direct actuators to respond to these deviations in such a way as to suppress the naturally occurring flow instabilities. Actuators which modify the boundary’s temperature or velocity are considered. The feedback controller can also be used to control flow patterns and generate complex dynamic behaviour at relatively low Rayleigh numbers.

scholarly journals Micropolar meets Newtonian in 3D. The Rayleigh–Bénard problem for large Prandtl numbers

Nonlinearity ◽  
2020 ◽  
Vol 33 (11) ◽  
pp. 5686-5732
Author(s):  
Piotr Kalita ◽  
Grzegorz Łukaszewicz
Keyword(s):  
Bénard Problem ◽  
Benard Problem ◽  
Prandtl Numbers ◽  
Rayleigh Benard

Numerical simulation of the turbulent Rayleigh–Bénard problem using subgrid modelling

1985 ◽  
Vol 158 ◽  
pp. 245-268 ◽  
Author(s):  
Thomas M. Eidson
Keyword(s):  
Numerical Simulation ◽  
Small Scale ◽  
Direct Simulation ◽  
Turbulent Natural Convection ◽  
Eddy Simulation ◽  
Subgrid Model ◽  
Short Period ◽  
Bénard Problem ◽  
Benard Problem ◽  
Rayleigh Benard

A numerical simulation of turbulent natural convection (the Rayleigh–Bénard problem) has been conducted using large-eddy-simulation (LES) methods and the results compared with several experiments. The development of the LES equation is outlined and discussed. The modelling of the small-scale turbulent motion (called subgrid modelling) is also discussed. The resulting LES equations are solved and data collected over a short period of time in a similar manner to the direct simulation of the governing conservation equations. An explicit, second-order accurate, finite-difference scheme is used to solve the equations. Various average properties of the resulting flow field are calculated from the data and compared with experimental data in the literature. The use of a subgrid model allows a higher value of Ra to be simulated than was previously possible with a direct simulation. The highest Ra successfully simulated was 2.5 × 106. The problems at higher values of Ra are discussed and suggestions for improvements made.

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