Q-tensor gradient flow with quasi-entropy and discretizations preserving physical constraints

10/21/2021
by   Yanli Wang, et al.
0

We propose and analyze numerical schemes for the gradient flow of Q-tensor with the quasi-entropy. The quasi-entropy is a strictly convex, rotationally invariant elementary function, giving a singular potential constraining the eigenvalues of Q within the physical range (-1/3,2/3). Compared with the potential derived from the Bingham distribution, the quasi-entropy has the same asymptotic behavior and underlying physics. Meanwhile, it is very easy to evaluate because of its simple expression. For the elastic energy, we include all the rotationally invariant terms. The numerical schemes for the gradient flow are built on the nice properties of the quasi-entropy. The first-order time discretization is uniquely solvable, keeping the physical constraints and energy dissipation, which are all independent of the time step. The second-order time discretization keeps the first two properties unconditionally, and the third with an O(1) restriction on the time step. These results also hold when we further incorporate a second-order discretization in space. Error estimates are also established for time discretization and full discretization. Numerical examples about defect patterns are presented to validate the theoretical results.

READ FULL TEXT

page 19

page 21

research
09/06/2023

Energy stable and maximum bound principle preserving schemes for the Q-tensor flow of liquid crystals

In this paper, we propose two efficient fully-discrete schemes for Q-ten...
research
09/07/2023

Second-order, Positive, and Unconditional Energy Dissipative Scheme for Modified Poisson-Nernst-Planck Equations

First-order energy dissipative schemes in time are available in literatu...
research
07/23/2020

An integral-based spectral method for inextensible slender fibers in Stokes flow

Every animal cell is filled with a cytoskeleton, a dynamic gel made of i...
research
11/04/2022

A numerical study of vortex nucleation in 2D rotating Bose-Einstein condensates

This article introduces a new numerical method for the minimization unde...
research
10/01/2019

Unconditionally energy stable DG schemes for the Swift-Hohenberg equation

The Swift-Hohenberg equation as a central nonlinear model in modern phys...
research
12/22/2020

Structure-preserving, energy stable numerical schemes for a liquid thin film coarsening model

In this paper, two finite difference numerical schemes are proposed and ...
research
09/13/2021

Thermodynamically consistent and positivity-preserving discretization of the thin-film equation with thermal noise

In micro-fluidics not only does capillarity dominate but also thermal fl...

Please sign up or login with your details

Forgot password? Click here to reset