TY - JOUR
T1 - A Second-Order Length-Preserving and Unconditionally Energy Stable Rotational Discrete Gradient Method for Oseen-Frank Gradient Flows
AU - Xu , Jie
AU - Yang , Xiaotian
AU - Yang , Zhiguo
JO - Communications in Computational Physics
VL - 2
SP - 369
EP - 394
PY - 2024
DA - 2024/03
SN - 35
DO - http://doi.org/10.4208/cicp.OA-2023-0191
UR - https://global-sci.org/intro/article_detail/cicp/22944.html
KW - Nematic liquid crystal, Oseen-Frank gradient flow, energy stability, length-preservation, rotational discrete gradient method.
AB - <p style="text-align: justify;">We present a second-order strictly length-preserving and unconditionally
energy-stable rotational discrete gradient (Rdg) scheme for the numerical approximation of the Oseen-Frank gradient flows with anisotropic elastic energy functional. Two
essential ingredients of the Rdg method are reformulation of the length constrained
gradient flow into an unconstrained rotational form and discrete gradient discretization for the energy variation. Besides the well-known mean-value and Gonzalez discrete gradients, we propose a novel Oseen-Frank discrete gradient, specifically designed for the solution of Oseen-Frank gradient flow. We prove that the proposed
Oseen-Frank discrete gradient satisfies the energy difference relation, thus the resultant Rdg scheme is energy stable. Numerical experiments demonstrate the efficiency
and accuracy of the proposed Rdg method and its capability for providing reliable
simulation results with highly disparate elastic coefficients.</p>