A POD-based reduced-order finite difference extrapolating model for the non-stationary incompressible Boussinesq equations

Advances in Difference Equations

Zhendong Luo¹ 

[1] School of Mathematics and Physics, North China Electric Power University, Beijing, China

关键词: proper orthogonal decomposition;    POD-based reduced-order finite difference extrapolating model;    non-stationary incompressible Boussinesq equations;    error estimate;    numerical simulation;   

DOI  :  10.1186/1687-1847-2014-272

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

A proper orthogonal decomposition (POD) method is used to establish a POD-based reduced-order finite difference (FD) extrapolating model with fully second-order accuracy for the non-stationary incompressible Boussinesq equations (NSIBEs). The error estimates of the POD-based reduced-order FD solutions obtained from the POD-based reduced-order FD extrapolating model are provided. The algorithm implementation for the POD-based reduced-order FD extrapolating model is given. A numerical experiment shows that the numerical results are consistent with the theoretical conclusions. Moreover, it is shown that the POD-based reduced-order FD extrapolating model is feasible and efficient for finding the numerical solutions for NSIBEs. MSC:76M20, 65M12, 65M15.

【 授权许可】

CC BY