On the convergence of an IEQ-based first-order semi-discrete scheme for the Beris-Edwards system

Journal Article · 29 November 2023 · ESAIM: Mathematical Modelling and Numerical Analysis

DOI: https://doi.org/10.1051/m2an/2023071 · OSTI ID:2222963

Weber, Franziska; Yue, Yukun

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 is a priori unclear 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.

• Sponsoring Organization: USDOE
• Grant/Contract Number: 1912854
• OSTI ID: 2222963
• Journal Information: ESAIM: Mathematical Modelling and Numerical Analysis, Journal Name: ESAIM: Mathematical Modelling and Numerical Analysis Vol. 57 Journal Issue: 6; ISSN 2822-7840
• Publisher: EDP SciencesCopyright Statement
• Country of Publication: Country unknown/Code not available
• Language: English