This talk will focus on a numerical approach based on the Invariant Quadratization Method(IEQ) to find solutions for a hydrodynamical system. We start with a toy model concerned with the parabolic type Q-tensor equations, design numerical schemes that keep energy dissipation law discretely, and analyze its properties. Then we present a convergence analysis of an unconditional energy-stable first-order semi-discrete numerical scheme intended for the hydrodynamic Q-tensor model. This model couples a Navier-Stokes system for the fluid flows and a parabolic type Q-tensor system governing the nematic liquid crystal director fields. We prove the stability properties of the scheme and show convergence to weak solutions of the coupled liquid crystal system. We will also be able to give you a brief on recent results on the existence and regularity of Beris-Edwards systems and other related models.

学术海报.pdf