A reduced finite difference scheme based on singular value decomposition and proper orthogonal decomposition for Burgers equation
A reduced finite difference scheme based on singular value decomposition and proper orthogonal decomposition for Burgers equation
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DOI：
10.1016/j.cam.2008.10.026
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发表时间：
2009-07
影响因子：
2.4
通讯作者：
Zhendong Luo;Xiaozhong Yang;Yan-jie Zhou
中科院分区：
文献类型：
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作者：
Zhendong Luo;Xiaozhong Yang;Yan-jie Zhou
针对Burgers方程提出了一种基于奇异值分解(SVD)和本征正交分解(POD)的降维优化有限差分格式(FDS)。分析了简化优化FDS的POD解与通常的有限差分解的误差估计。对空腔流动的数值模拟结果表明，简化优化FDS的POD解与通常FDS的解的误差与理论结果一致。此外，还表明了简化的优化FDS是可行和有效的。
In this article, a reduced optimizing finite difference scheme (FDS) based on singular value decomposition (SVD) and proper orthogonal decomposition (POD) for Burgers equation is presented. Also the error estimates between the usual finite difference solution and the POD solution of reduced optimizing FDS are analyzed. It is shown by considering the results obtained for numerical simulations of cavity flows that the error between the POD solution of reduced optimizing FDS and the solution of the usual FDS is consistent with theoretical results. Moreover, it is also shown that the reduced optimizing FDS is feasible and efficient.