TY - JOUR
T1 - Unconditional Long Time $\text{H}^1$-Stability of a Velocity-Vorticity-Temperature Scheme for the $2\text{D}$-Boussinesq System
AU - Akbas , Mine
JO - Advances in Applied Mathematics and Mechanics
VL - 5
SP - 1166
EP - 1195
PY - 2020
DA - 2020/07
SN - 12
DO - http://doi.org/10.4208/aamm.OA-2019-0122
UR - https://global-sci.org/intro/article_detail/aamm/17744.html
KW - Long time stability, incompressible flow, vorticity equation, finite element method.
AB - <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>