A Sequential Regularization Method for Time-Dependent Incompressible Navier--Stokes Equations
SIAM Journal on Numerical Analysis
Approximation of Liquid Crystal Flows
SIAM Journal on Numerical Analysis
Fourier Spectral Approximation to a Dissipative System Modeling the Flow of Liquid Crystals
SIAM Journal on Numerical Analysis
An adaptive homotopy multi-grid method for molecule orientations of high dimensional liquid crystals
Journal of Computational Physics
Journal of Computational Physics
3D phase-field simulations of interfacial dynamics in Newtonian and viscoelastic fluids
Journal of Computational Physics
Finite element approximation of nematic liquid crystal flows using a saddle-point structure
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.49 |
In this paper, we present a C^0 finite element method for a 2D hydrodynamic liquid crystal model which is simpler than existing C^1 element methods and mixed element formulation. The energy law is formally justified and the energy decay is used as a validation tool for our numerical computation. A splitting method combined with only a few fixed point iteration for the penalty term of the director field is applied to reduce the size of the stiffness matrix and to keep the stiffness matrix time-independent. The latter avoids solving a linear system at every time step and largely reduces the computational time, especially when direct linear system solvers are used. Our approach is verified by comparing its computational results with those obtained by C^1 elements and by mixed formulation. Through numerical experiments of a few other splittings and explicit-implicit strategies, we recommend a fast and reliable algorithm for this model. A number of examples are computed to demonstrate the algorithm.