@Article{AAMM-12-5,
author = {Mine, Akbas},
title = {Unconditional Long Time $\text{H}^1$-Stability of a Velocity-Vorticity-Temperature Scheme for the $2\text{D}$-Boussinesq System},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2020},
volume = {12},
number = {5},
pages = {1166--1195},
abstract = {<p style="text-align: justify;">This paper proposes, analyzes and tests a velocity-vorticity-temperature (VVT) scheme for incompressible, non-isothermal fluid flow. VVT consists of complementing of the usual velocity-pressure-temperature system with the vorticity equation, coupling the systems through the convective terms. The proposed scheme uses BDF2LE time stepping, and a finite element spatial discretization. At each time step, the velocity-pressure equation, the vorticity equation and the temperature equation are all decoupled. A full analysis of the method is given that proves unconditional long-time $\text{H}^1$-stability, and shows the optimal convergence both in time and space. Theoretical convergence results are confirmed by a numerical test, and the effectiveness of the algorithm is revealed on a benchmark problem for Marsigli flow.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.OA-2019-0122},
url = {https://global-sci.com/article/73072/unconditional-long-time-texth1-stability-of-a-velocity-vorticity-temperature-scheme-for-the-2textd-boussinesq-system}
}