A Second-Order Length-Preserving and Unconditionally Energy Stable Rotational Discrete Gradient Method for Oseen-Frank Gradient Flows
Year: 2024
Author: Jie Xu, Xiaotian Yang, Zhiguo Yang
Communications in Computational Physics, Vol. 35 (2024), Iss. 2 : pp. 369–394
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2023-0191
Communications in Computational Physics, Vol. 35 (2024), Iss. 2 : pp. 369–394
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 26
Keywords: Nematic liquid crystal Oseen-Frank gradient flow energy stability length-preservation rotational discrete gradient method.