基于校正技术的流动耦合脂质囊泡模型的线性能量稳定格式  

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

作　　者：李琦 陈荟奕 李玉超 LI Qi;CHEN Huiyi;LI Yuchao(School of Science,Chang'an University,Xi'an 710064,China)

机构地区：[1]长安大学理学院,陕西西安710064

出　　处：《浙江大学学报(理学版)》2025年第2期238-251,共14页Journal of Zhejiang University(Science Edition)

基　　金：国家自然科学基金资助项目(12101073);陕西数理基础科学研究项目(22JSQ021);长安大学中央高校基本科研业务费专项(300102123103);中国博士后科学基金资助项目(2023M730359).

摘　　要：主要研究了Navier-Stokes方程与脂质囊泡弹性弯曲能模型耦合系统的高效数值逼近。为准确有效地求解此复杂系统,提出了一种基于时间依赖辅助变量的完全解耦、线性、二阶时间精确算法,采用压力投影法解耦计算Navier-Stokes方程中的速度场和压力场,并给出了算法的实现步骤;对离散格式的能量稳定性和唯一可解性进行了理论证明。为进一步增强原始能量和修正能量之间的一致性,引入了一种简单有效的能量校正技术。通过二维数值实验证明了所提出的算法精度高、能量稳定。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.

关 键 词：相场模型 弹性弯曲能 完全解耦 校正能量 

分 类 号：O212.7[理学—概率论与数理统计]