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.
Echo state network for two-dimensional turbulent moist Rayleigh-Bénard convection