利用本征正交分解的非线性Galerkin降维方法  

Nonlinear Galerkin Method for Dimension Reduction Using Proper Orthogonal Decomposition

作　　者：康伟[1] 张家忠[1] 李凯伦[1] 

机构地区：[1]西安交通大学能源与动力工程学院,西安710049

出　　处：《西安交通大学学报》2011年第11期58-62,67,共6页Journal of Xi'an Jiaotong University

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.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 Galerkin method using POD modes is chosen to approximate the nonlinear partial differential equations for fluids and reduce the system from infinite dimension to lower dimension.The flow past NACA0012 airfoil at Re=200 and the attack angle of 20° is simulated for low-dimensional modeling analysis to verify the efficiency of the method.The results show that because the effect of high-order modes is taken into account,the present method enables to give an accurate description of the system＇s dynamic behaviors and preserve the topological structure of the system with fewer modes,compared with conventional POD method.

关 键 词：本征正交分解 近似惯性流形 动力系统 降维 非线性 

分 类 号：O241[理学—计算数学]