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Title: On the convergence of an IEQ-based first-order semi-discrete scheme for the Beris-Edwards system
We present a convergence analysis of an unconditionally energy-stable first-order semi-discrete numerical scheme designed for a hydrodynamic Q-tensor model, the so-called Beris-Edwards system, based on the Invariant Energy Quadratization Method (IEQ). The model consists of the Navier–Stokes equations for the fluid flow, coupled to the Q-tensor gradient flow describing the liquid crystal molecule alignment. By using the Invariant Energy Quadratization Method, we obtain a linearly implicit scheme, accelerating the computational speed. However, this introduces an auxiliary variable to replace the bulk potential energy and it isa prioriunclear whether the reformulated system is equivalent to the Beris-Edward system. In this work, we prove stability properties of the scheme and show its convergence to a weak solution of the coupled liquid crystal system. We also demonstrate the equivalence of the reformulated and original systems in the weak sense.  more » « less
Award ID(s):
1912854
PAR ID:
10483380
Author(s) / Creator(s):
;
Publisher / Repository:
EDP Sciences
Date Published:
Journal Name:
ESAIM: Mathematical Modelling and Numerical Analysis
Volume:
57
Issue:
6
ISSN:
2822-7840
Page Range / eLocation ID:
3275 to 3302
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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