A fully-decoupled discontinuous Galerkin method for the nematic liquid crystal flows with SAV approach

Zheng, Zhaohui; Zou, Guang‐an; Wang, Bo; Zhao, Wenju

doi:10.1016/j.cam.2023.115207

Cited by 10 publications

(2 citation statements)

References 47 publications

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“…In what follows, we prove the existence and uniqueness of the scheme (17a,b)–(20), the similar skills can be found in References 35–37, 48–52.…”

Section: Fully Discrete Schemessupporting

confidence: 57%

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Unconditionally stable fully‐discrete finite element numerical scheme for active fluid model

Wang,

Zhang,

Zou

2024

Numerical Methods in Fluids

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In this paper, we propose a linear, decoupled, unconditionally stable fully‐discrete finite element scheme for the active fluid model, which is derived from the gradient flow approach for an effective non‐equilibrium free energy. The developed scheme is employed by an implicit‐explicit treatment of the nonlinear terms and a second‐order Gauge–Uzawa method for the decoupling of computations for the velocity and pressure. We rigorously prove the unique solvability and unconditional stability of the proposed scheme. Several numerical tests are presented to verify the accuracy, stability, and efficiency of the proposed scheme. We also simulate the self‐organized motion under the various external body forces in 2D and 3D cases, including the motion direction of active fluid from disorder to order. Numerical results show that the scheme has a good performance in accurately capturing and handling the complex dynamics of active fluid motion.

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“…In what follows, we prove the existence and uniqueness of the scheme (17a,b)–(20), the similar skills can be found in References 35–37, 48–52.…”

Section: Fully Discrete Schemessupporting

confidence: 57%

“…where U(u) = 𝛼 2 u 2 + 𝛽 4 u 4 and G(u) = −f ⋅ u. Then the active fluid model can be obtained by the minimization of the free energy functional ℱ (p, u), considering the Equations ( 2) and (3) with 𝜂 = (p, u) and applying the gradient flow approach, [34][35][36][37] we have…”

Section: The Model Systemmentioning

confidence: 99%