非定常微极流体方程的速度校正投影方法  

Velocity-Correction Projection Method for the Time-Dependent Micropolar Fluid Equations

作　　者：阿妮柯孜·奥斯曼 冯新龙[1] 刘德民[1] ANIKEZI Aosiman;FENG Xinlong;LIU Demin(School of Mathematics and System Sciences,Xinjiang University,Urumqi Xinjiang 830017,China)

机构地区：[1]新疆大学数学与系统科学学院,新疆乌鲁木齐830017

出　　处：《新疆大学学报（自然科学版）（中英文）》2023年第2期150-159,共10页Journal of Xinjiang University(Natural Science Edition in Chinese and English)

基　　金：国家自然科学基金“铝电解槽中多介质磁流体动力学方程的高效数值方法研究”(12061075);新疆重点实验室开放课题“两相不可压磁流体动力学方程高效算法研究”(2022D04014)。

摘　　要：研究了二维和三维非定常微极流体方程的速度校正投影方法.采用一阶和二阶后向差分格式进行时间离散及协调有限元进行空间离散,给出了一阶和二阶时间半离散速度校正投影方法的无条件稳定性和一阶时间半离散格式的误差估计以及相应的全离散格式,证明了一阶全离散格式的无条件稳定性.最后,通过数值算例验证了该方法的有效性.The velocity-correction projection method for the 2D/3D time-dependent micropolar fluid equations is considered.In this method,the first-order and second-order backward difference schemes are applied for time discretization and conforming finite element is adopted for spatial discretization.The unconditional stability of the first-order and second-order time semi-discrete velocity-correction projection methods are given,and the error estimation of the first-order semi-discrete scheme is analyzed.The stability analysis of the first-order fully discrete scheme is also given.Finally,several numerical examples are presented to show the efficiency of the proposed method.

关 键 词：微极流体方程 速度校正投影方法 协调有限元 稳定性分析 误差估计 

分 类 号：O241[理学—计算数学]