TY - JOUR
T1 - Approximation of the Long-Term Dynamics of the Dynamical System Generated by a 3D NS-$α$ System with Phase Transition
AU - Medjo , T. Tachim
AU - Tone , F.
JO - International Journal of Numerical Analysis and Modeling
VL - 3
SP - 307
EP - 339
PY - 2018
DA - 2018/03
SN - 15
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/12518.html
KW - Navier–Stokes-$α$, phase transition, attractors, implicit Euler scheme, Gronwall Lemma.
AB - <p style="text-align: justify;">In this article we study an approximate model for a binary fluid flow in a three-dimensional
bounded domain. The governing equations consist of the Allen–Cahn equation for
the order (phase) parameter $\phi$ coupled with the Navier–Stokes-$α$ (NS-$α$) system for the velocity $u$.
We discretize these equations in time using the implicit Euler scheme and we prove that the global
attractors generated by the numerical scheme converge to the global attractor of the continuous
system as the time-step approaches zero.<br/></p>