The Bénard Problem for Slightly Compressible Materials: Existence and Linear Instability

2019 ◽  
Vol 16 (1) ◽  
Author(s):  
Andrea Corli ◽  
Arianna Passerini
Keyword(s):  
Linear Instability ◽  
Slightly Compressible ◽  
Bénard Problem ◽  
Benard Problem ◽  
Compressible Materials

scholarly journals Bénard Problem for Slightly Compressible Fluids: Existence and Nonlinear Stability in 3D

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Arianna Passerini
Keyword(s):  
Pressure Field ◽  
Fluid Model ◽  
Classical Model ◽  
Compressible Fluids ◽  
Heat Conducting ◽  
Regular Solutions ◽  
New Approach ◽  
Slightly Compressible ◽  
Bénard Problem ◽  
Benard Problem

This paper shows the existence, uniqueness, and asymptotic behavior in time of regular solutions (a la Ladyzhenskaya) to the Bénard problem for a heat-conducting fluid model generalizing the classical Oberbeck–Boussinesq one. The novelty of this model, introduced by Corli and Passerini, 2019, and Passerini and Ruggeri, 2014, consists in allowing the density of the fluid to also depend on the pressure field, which, as shown by Passerini and Ruggeri, 2014, is a necessary request from a thermodynamic viewpoint when dealing with convective problems. This property adds to the problem a rather interesting mathematical challenge that is not encountered in the classical model, thus requiring a new approach for its resolution.

On the two-component Benard problem a numerical solution

1975 ◽  
Vol 80 (1) ◽  
pp. 76-88 ◽  
Author(s):  
J.C. Legros ◽  
D. Longree ◽  
G. Chavepeyer ◽  
J.K. Platten
Keyword(s):  
Numerical Solution ◽  
Two Component ◽  
Bénard Problem ◽  
Benard Problem

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.

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