Linear energy-stable scheme based on correction technique for the flow-coupled model of lipid vesicles

• Published in: Zhejiang da xue xue bao. Journal of Zhejiang University. Sciences edition. Li xue ban Vol. 52; no. 2; p. 238
• Main Authors: Li, Qi, Chen, Huiyi, Li, Yuchao
• Format: Journal Article
• Language: Chinese; English
• Published: Hangzhou Zhejiang University 01.03.2025
• Subjects: Algorithms; Complex systems; Elastic bending; Fluid flow; Lipids; Mathematical analysis; Navier-Stokes equations; Stability; Time dependence; Velocity distribution; Vesicles
• ISSN: 1008-9497
• DOI: 10.3785/j.issn.1008-9497.2025.02.008

This paper primarily investigates the efficient numerical approximation of a coupled system of Navier-Stokes equations and the elastic bending energy model of lipid vesicles. To accurately and effectively solve this complex system, a fully decoupled, linear, second-order time-accurate method based on the time-dependent auxiliary variable approach is proposed. The pressure projection method is employed to decouple the computation of the velocity field and pressure field in the Navier-Stokes equations. The detailed implementation of the algorithm is presented in this paper, and the energy stability and uniqueness of the discrete scheme are rigorously proved theoretically. To further enforce the consistency between the original energy and the modified energy, a simple and effective energy correction technique is introduced. The accuracy and energy stability of the proposed numerical scheme are validated through two-dimensional numerical experiments.