Low-dimensional dynamical system for Rayleigh-Bénard convection subjected to magnetic field

2013 ◽  
Vol 113 (12) ◽  
pp. 124902 ◽  
Author(s):  
Hiroshi Gotoda ◽  
Riyota Takeuchi ◽  
Yuta Okuno ◽  
Takaya Miyano
Keyword(s):  
Magnetic Field ◽  
Dynamical System ◽  
Bénard Convection ◽  
Benard Convection ◽  
Dimensional Dynamical System ◽  
Low Dimensional ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

APPROXIMATION OF THE STATIONARY STATISTICAL PROPERTIES OF THE DYNAMICAL SYSTEM GENERATED BY THE TWO-DIMENSIONAL RAYLEIGH–BÉNARD CONVECTION PROBLEM

2011 ◽  
Vol 09 (04) ◽  
pp. 421-446 ◽  
Author(s):  
FLORENTINA TONE ◽  
XIAOMING WANG
Keyword(s):  
Dynamical System ◽  
Global Attractors ◽  
Statistical Properties ◽  
Two Dimensional ◽  
Time Step ◽  
Bénard Convection ◽  
Benard Convection ◽  
Convection Problem ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

In this article, we consider a temporal linear semi-implicit approximation of the two-dimensional Rayleigh–Bénard convection problem. We prove that the stationary statistical properties as well as the global attractors of this linear semi-implicit scheme converge to those of the 2D Rayleigh–Bénard problem as the time step approaches zero.

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