大气污染模型的特征投影分解优化有限体积元方法  

Proper Orthogonal Decomposition Optimized Finite Volume Element Method for Air Pollution Model

作　　者：冯尚[1] 赵巨东[2] FENG Shang ZHAO Ju-dong(Inner Mongolia Electronic Information Vocational Technology College, Hohhot 014030 College of Sciences, Inner Mongolia University of Technology, Hohhot 010051 ,China)

机构地区：[1]内蒙古电子信息职业技术学院,内蒙古呼和浩特010070 [2]内蒙古工业大学理学院,内蒙古呼和浩特010051

出　　处：《内蒙古师范大学学报（自然科学汉文版）》2017年第3期329-333,共5页Journal of Inner Mongolia Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(51268040)

摘　　要：将特征投影分解技术引入有限体积元方法,提出一种针对大气污染问题的微分方程模型的优化数值方法,并分析了优化方法的收敛性.该方法利用最初较短时间内的数值解作瞬像集,建立特征投影分解基底,在原有体积元格式基础上构造一种降阶优化格式,计算剩余时间段的数值解.数值实验结果表明,相比原有限体积元方法,优化有限体积元法降低了离散方程组的未知量个数,节省了计算消耗,能够快速预测污染现象,从而验证了该方法的可行性和有效性.The technique of proper orthogonal decomposition is introduced in finite volume element method to construct a kind of optimized numerical method. The convergence of the optimized numerical method is analyzed. This method use numerical solutions on a premier short period of time as a snapshot set to build a proper orthogonal decomposition bases, then construct a reduced order optimized scheme based on the original finite volume element scheme to calculate the numerical solutions on the remaining period of time. The numerical experiment results show that, compared the original finite volume element method,the optimized finite volume element method,this method reduced the unknown number of discrete equation system, saved the calculation consumption, quickly predict the pollution phenomenon, and the feasibility and effectiveness of the method are verified.

关 键 词：大气污染模型 特征投影分解 有限体积元法 误差分析 

分 类 号：O241.82[理学—计算数学]