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

Tone, F; Wang, XM; Wirosoetisno, D

Abstract

We consider a two-dimensional model of double-diffusive convection and its time discretisation using a second-order scheme (based on backward differentiation formula for the time derivative) which treats the non-linear term explicitly. Uniform bounds on the solutions of both the continuous and discrete models are derived (under a timestep restriction for the discrete model), proving the existence of attractors and invariant measures supported on them. As a consequence, the convergence of the attractors and long time statistical properties of the discrete model to those of the continuous one in the limit of vanishing timestep can be obtained following established methods.

Citation

Tone, F., Wang, X., & Wirosoetisno, D. (2014). Long-time dynamics of 2d double-diffusive convection: analysis and/of numerics. Numerische Mathematik, 130(3), 541-566. https://doi.org/10.1007/s00211-014-0670-9

• Journal Article Type: Article
• Acceptance Date: Sep 23, 2014
• Online Publication Date: Nov 15, 2014
• Publication Date: Nov 15, 2014
• Deposit Date: Sep 29, 2016
• Publicly Available Date: Sep 13, 2017
• Journal: Numerische Mathematik
• Print ISSN: 0029-599X
• Electronic ISSN: 0945-3245
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 130
• Issue: 3
• Pages: 541-566
• DOI: https://doi.org/10.1007/s00211-014-0670-9
• Public URL: https://durham-repository.worktribe.com/output/1396409