POD reduced-order unstructured mesh modelling applied to 2 D and 3 D fluid flow
POD reduced-order unstructured mesh modelling applied to 2 D and 3 D fluid flow
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发表时间：
2012
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通讯作者：
J. Du;F. Fang;C. C. Pain-C.;I. M. Navon;J. Zhu
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作者：
J. Du;F. Fang;C. C. Pain-C.;I. M. Navon;J. Zhu
提出了一种实现复杂网格数值模型(如有限元非结构网格模型)降维模型的新方案。将完整模型的矩阵和源项向量投影到约简基上。使用本征正交分解(POD)来形成还原碱基。即使使用复杂的控制方程、离散化方法和非线性参数，降阶建模代码也很容易实现。重要的是，模型降阶代码独立于完整模型代码的实现细节。对于非线性问题，基于离散的方程组具有多项式表示，从而可以通过预先形成的矩阵的求和来创建的假设，使用摄动法来帮助加速矩阵方程的组装过程。本文应用新方法，在非结构网格有限元流体流动模型上实现了POD降阶模型，并将其应用于三维流动。对全阶有限元解与降阶模型POD解的误差进行了估计。论证了降阶模型应用于三维流体流动的可行性和准确性。
A new scheme for implementing a reduced order model for complex meshbased numerical models (e.g. finite element unstructured mesh models), is presented. The matrix and source term vector of the full model are projected onto the reduced bases. The proper orthogonal decomposition (POD) is used to form the reduced bases. The reduced order modelling code is simple to implement even with complex governing equations, discretization methods and non-linear parameterizations. Importantly, the model order reduction code is independent of the implementation details of the full model code. For nonlinear problems, a perturbation approach is used to help accelerate the matrix equation assembly process based on the assumption that the discretized system of equations has a polynomial representation and can thus be created by a summation of pre-formed matrices. In this paper, by applying the new approach, the POD reduced order model is implemented on an unstructured mesh finite element fluid flow model, and is applied to 3D flows. The error between the full order finite element solution and the reduced order model POD solution is estimated. The feasibility and accuracy of the reduced order model applied to 3D fluid flows are demonstrated.