Second Order, Linear, and Unconditionally Energy Stable Schemes for a Hydrodynamic Model of Smectic-A Liquid Crystals

Chen, Rui; Yang, Xiaofeng; Zhang, Hui

doi:10.1137/17m1119834

Cited by 23 publications

(5 citation statements)

References 86 publications

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“…The invariant energy quadratisation (IEQ) method, proposed by Yang [53], has been applied to different phase field models [5,12,20,49,[54][55][56][57][58][59][60]67]. In this approach, all the nonlinear terms are treated implicitly and the free energy has to be bounded from below.…”

Section: Introductionmentioning

confidence: 99%

Modeling and Simulation of a Ternary System for Macromolecular Microsphere Composite Hydrogels

Ji¹

2021

EAJAM

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In this paper, we study a ternary system for macromolecular microsphere composite (MMC) hydrogels. Assuming that the graft chains are distributed randomly around the macromolecular microspheres, a phase transition model was constructed. The stabilised-scalar auxiliary variable (S-SAV) approach is used to present a first-order energy stable scheme for solving the nonlinear system. Some numerical experiments are carried out to show the accuracy of the scheme, including the mass conservation of the volume fractions, the decrease in the modified energy, and the influence of different parameters.

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Section: Introductionmentioning

confidence: 99%

Modeling and Simulation of a Ternary System for Macromolecular Microsphere Composite Hydrogels

Ji¹

2021

EAJAM

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“…( 20 )) become which together have the form , where we have included an arbitrary constant, assigned the f curv differing elastic coefficients, and absorbed into each coefficient. Moreover, for simplifying choices of constants, this becomes , which is an existing model free energy density for smectics 7 , 13 , 71 , 97 . We could also choose to write this in terms of a layer displacement u = ϕ / q 0 , making this free energy .…”

Section: Methodsmentioning

confidence: 99%

“…which is an existing model free energy density for smectics 7,13,71,97 . We could also choose to write this in terms of a layer displacement u = ϕ/q 0 , making this free energy…”

Section: Lagrange Multipliersmentioning

confidence: 99%

Complex-tensor theory of simple smectics

et al. 2023

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Matter self-assembling into layers generates unique properties, including structures of stacked surfaces, directed transport, and compact area maximization that can be highly functionalized in biology and technology. Smectics represent the paradigm of such lamellar materials — they are a state between fluids and solids, characterized by both orientational and partial positional ordering in one layering direction, making them notoriously difficult to model, particularly in confining geometries. We propose a complex tensor order parameter to describe the local degree of lamellar ordering, layer displacement and orientation of the layers for simple, lamellar smectics. The theory accounts for both dislocations and disclinations, by regularizing singularities within defect cores and so remaining continuous everywhere. The ability to describe disclinations and dislocation allows this theory to simulate arrested configurations and inclusion-induced local ordering. This tensorial theory for simple smectics considerably simplifies numerics, facilitating studies on the mesoscopic structure of topologically complex systems.

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“…The SAV approach is built on the the invariant energy quadratization (IEQ) approach, so it inherits all advantages of the IEQ approach and conquers most of its weaknesses such as the IEQ method will lead to systems with variable coefficients and it requires that the energy density function is bounded from below rather than energy. For the application of IEQ method, more details are available in article [18][19][20][21][22]. The SAV method also keeps its shortcomings that is only the modified energy is unconditionally stable but not the original one.…”

Section: Introductionmentioning

confidence: 99%

Second‐order scalar auxiliary variable Fourier‐spectral method for a liquid thin film coarsening model

Zhang,

Dong,

Zhang

2023

Math Methods in App Sciences

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In this paper, we propose and analyze a second‐order accurate (in time) numerical scheme for the droplet liquid film coarsening model by using the scalar auxiliary variable (SAV) method, and the Fourier‐spectral method is used in space. The scheme is linear; thus, it could be solved very efficiently. Meanwhile, due to the application of SAV approach, the unconditional energy stability of the numerical scheme is also derived, without any restriction on the time step size. In addition, we also provide a rigorous error estimate that shows that our second‐order numerical scheme with Fourier‐spectral method in space converges with order , where and are time and space step sizes, respectively. Finally, a few numerical experiments are performed, which confirms the efficiency and accuracy of the proposed scheme, including the tests of the convergence, the mass conservation and the decrease of the energy. The simulation of coarsening process with time is also observed.

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Second Order, Linear, and Unconditionally Energy Stable Schemes for a Hydrodynamic Model of Smectic-A Liquid Crystals

Cited by 23 publications

References 86 publications

Modeling and Simulation of a Ternary System for Macromolecular Microsphere Composite Hydrogels

Modeling and Simulation of a Ternary System for Macromolecular Microsphere Composite Hydrogels

Complex-tensor theory of simple smectics

Second‐order scalar auxiliary variable Fourier‐spectral method for a liquid thin film coarsening model

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