| 利用本征正交分解的非线性Galerkin降维方法 |
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| 引用本文： | 康伟,张家忠,李凯伦.利用本征正交分解的非线性Galerkin降维方法[J].西安交通大学学报,2011,45(11):58-62,67. |
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| 作者姓名： | 康伟 张家忠 李凯伦 |
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| 作者单位： | 西安交通大学能源与动力工程学院,710049,西安 |
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| 摘 要： | 提出了一种利用本征正交分解(POD)的非线性Galerkin方法,用于复杂流体动力系统的低维建模.该方法将满足流场边界条件的正交基(POD模态)张成的完备空间分解为有限维(低阶模态)子空间和无限维(高阶模态)子空间,并采用近似惯性流形逼近高阶模态和低阶模态的作用关系,用低阶分量来表示高阶分量,将无穷维流体动力系统降维成有限维动力系统.以雷诺数为200、攻角为20°时的NACA0012翼型绕流流动问题为例进行了低维建模分析,结果表明:由于考虑了高阶模态的影响,且不改变原系统的拓扑结构,因此该降维方法能够用较少的模态数来获得准确的动力学描述,弥补了传统POD降维方法由于忽略高阶模态影响而出现的不足,由此验证了该方法的有效性.
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| 关 键 词： | 本征正交分解 近似惯性流形 动力系统 降维 非线性 |
Nonlinear Galerkin Method for Dimension Reduction Using Proper Orthogonal Decomposition |
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| KANG Wei,ZHANG Jiazhong,LI Kailun.Nonlinear Galerkin Method for Dimension Reduction Using Proper Orthogonal Decomposition[J].Journal of Xi'an Jiaotong University,2011,45(11):58-62,67. |
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| Authors: | KANG Wei ZHANG Jiazhong LI Kailun |
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| Institution: | (School of Energy and Power Engineering,Xi′an Jiaotong University,Xi′an 710049,China) |
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| Abstract: | Nonlinear Galerkin method using POD modes is presented for low-dimensional modeling of the fluid dynamical system.The method splits the complete space spanned by the POD modes satisfying the boundary condition of the flow field into two subspaces-a finite-dimensional one spanned by low-order modes and its complement spanned by high-order modes.Then the interaction nature between the low-order modes and high-order modes is considered via the introduction of approximate inertial manifold.Furthermore,nonlinear... |
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| Keywords: | proper orthogonal decomposition approximate inertial manifold dynamic system dimension reduction nonlinearity |
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