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We consider a two-dimensional model of double-diffusive convection and itstime discretisation using a second-order scheme which treat the nonlinear termexplicitly (backward differentiation formula with a one-leg method). Uniformbounds on the solutions of both the continuous and discrete models are derived(under a timestep restriction for the discrete model), proving the existence ofattractors and invariant measures supported on them. As a consequence, theconvergence of the attractors and long time statistical properties of thediscrete model to those of the continuous one in the limit of vanishingtimestep can be obtained following established methods.

Long-time dynamics of 2d double-diffusive convection: analysis and/of numerics