Approximation of the Long-Term Dynamics of the Dynamical System Generated by a 3D NS-$α$ System with Phase Transition
Year: 2018
Author: T. Tachim Medjo, F. Tone
International Journal of Numerical Analysis and Modeling, Vol. 15 (2018), Iss. 3 : pp. 307–339
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2018-IJNAM-12518
International Journal of Numerical Analysis and Modeling, Vol. 15 (2018), Iss. 3 : pp. 307–339
Published online: 2018-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 33
Keywords: Navier–Stokes-$α$ phase transition attractors implicit Euler scheme Gronwall Lemma.