非定常Stokes方程的降阶稳定化CN有限体积元外推模型  

A Reduced-Order Stabilized CNFVE Extrapolating Model for Non-Stationary Stokes Equations

作　　者：腾飞[1] 罗振东[2] 

机构地区：[1]凯里学院数学科学学院,贵州凯里556011 [2]华北电力大学数理学院,北京102206

出　　处：《应用数学和力学》2014年第9期986-1001,共16页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11271127);贵州省教育厅自然科学研究项目(黔教合KY字[2013]207)~~

摘　　要：利用稳定化的Crank-Nicolson(CN)有限体积元方法和特征投影分解方法,建立非定常Stokes方程的一种自由度很少、精度足够高的降阶稳定化CN有限体积元外推模型,并给出这种降阶稳定化CN有限体积元外推模型解的误差估计和算法的实现.最后用数值例子说明数值结果与理论结果相吻合,并阐明这种降阶稳定化CN有限体积元外推模型的优越性.A reduced-order stabilized Crank-Nicolson finite volume element （SCNFVE） extrapolating model with sufficiently high accuracy and few degrees of freedom for non-stationary Stokes equations was established by means of the SCNFVE method and the proper orthogonal decompostion （POD） technique. The error estimates of the reduced-order approximate solutions and the algorithm implementation for the reduced-order SCNFVE extrapolating model were provided. Finally, a numerical example of conduit flow indicates that the results of the proposed model are consistent with those of the theoretical solution. Moreover, the advantages of lower computation complexity and higher calculation accuracy of the reduced-order SCNFVE extrapolating model are shown in comparison with the classical methods.

关 键 词：稳定化CN有限体积元方法 特征投影分解方法 非定常STOKES方程 误差估计 

分 类 号：O242.21[理学—计算数学]