Variational Multiscale Proper Orthogonal Decomposition: Navier-Stokes Equations
Variational Multiscale Proper Orthogonal Decomposition: Navier-Stokes Equations
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DOI：
10.1002/num.21835
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发表时间：
2014-03-01
影响因子：
3.9
通讯作者：
Wang, Zhu
中科院分区：
文献类型：
--
作者：
Iliescu, Traian;Wang, Zhu
建立了湍流不可压Navier-Stokes方程的变分多尺度本征正交分解降阶模型。在基本有限元近似和POD基生成的两个假设下，给出了全离散的误差分析。考虑了各种误差的影响：空间离散误差(由有限元离散引起)、时间离散误差(由后向欧拉法引起)和POD截断误差。对雷诺数为圆柱体的三维湍流流动的数值试验表明，新模型的物理精度比标准Galerkin和混合长度POD ROMS有所提高。该模型具有较高的计算效率。最后，通过对二维N-S问题的数值模拟，验证了理论误差估计的正确性。©2013 Wiley期刊，Inc.Numer方法偏差式30：641-663,2014
We develop a variational multiscale proper orthogonal decomposition (POD) reduced‐order model (ROM) for turbulent incompressible Navier‐Stokes equations. Under two assumptions on the underlying finite element approximation and the generation of the POD basis, the error analysis of the full discretization of the ROM is presented. All error contributions are considered: the spatial discretization error (due to the finite element discretization), the temporal discretization error (due to the backward Euler method), and the POD truncation error. Numerical tests for a three‐dimensional turbulent flow past a cylinder at Reynolds number show the improved physical accuracy of the new model over the standard Galerkin and mixing‐length POD ROMs. The high computational efficiency of the new model is also showcased. Finally, the theoretical error estimates are confirmed by numerical simulations of a two‐dimensional Navier‐Stokes problem. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 641–663, 2014