非定常微极流体方程的一阶算子分裂方法

数学物理学报 ›› 2026, Vol. 46 ›› Issue (6): 2264-2276.

非定常微极流体方程的一阶算子分裂方法

阿妮柯孜·奥斯曼^*()

喀什大学新疆喀什 844000

收稿日期:2025-08-20 修回日期:2026-09-15 出版日期:2026-12-26 发布日期:2026-08-14
通讯作者: 阿妮柯孜·奥斯曼 E-mail:2720187148@qq.com
基金资助:
微极流体方的有限元方研究((2024) 2920)

First-Order Operator Splitting Method for Unsteady Micropolar Fluid Equations

Aosiman Anikezi^*()

Kashi University, Xinjiang Kashi 844000

Received:2025-08-20 Revised:2026-09-15 Online:2026-12-26 Published:2026-08-14
Contact: Aosiman Anikezi E-mail:2720187148@qq.com
Supported by:
Research on Finite Element Methods for Micropolar Fluid Equations((2024) 2920)

摘要/Abstract

摘要：

该文讨论 2D/3D 非定常微极流体方程的一阶算子分裂方法. 该方法在时间方向用一阶欧拉格式离散, 空间方向用协调有限元方法离散. 该文给出了一阶半离散算子分裂方法的无条件稳定性和误差估计, 并提出了相应的全离散格式. 证明了一阶全离散格式的无条件稳定性结论. 最后, 通过数值算例验证了该方法的准确性和有效性.

关键词: 微极流体方程, 算子分裂法, 有限元法, 稳定性分析, 误差估计

Abstract:

This paper discusses the first-order operator splitting method for 2D/3D unsteady micropolar fluid equations. The method is discretized by the first-order Euler scheme in the time direction and the coordinated finite element method in the space direction. The unconditional stability and error estimation of the first-order semi-discrete operator splitting method are given, and the corresponding fully discrete scheme is proposed. The unconditional stability conclusion of the first-order fully discrete scheme is proved. Finally, the accuracy and effectiveness of the method are verified by numerical examples.

Key words: microscale fluid equations, operator splitting method, finite element method, stability analysis, error estimation

中图分类号:

阿妮柯孜·奥斯曼. 非定常微极流体方程的一阶算子分裂方法[J]. 数学物理学报, 2026, 46(6): 2264-2276.

Aosiman Anikezi. First-Order Operator Splitting Method for Unsteady Micropolar Fluid Equations[J]. Acta mathematica scientia,Series A, 2026, 46(6): 2264-2276.

图/表 4

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