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论文:2017,Vol:35,Issue(5):834-842 |
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引用本文： |
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王晨, 白俊强, Jan S Hesthaven, 邱亚松, 杨体浩. 一种针对带参数非定常问题的非嵌入式降阶模型[J]. 西北工业大学学报 |
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Wang Chen, Bai Junqiang, Jan S Hesthaven, Qiu Yasong, Yang Tihao. A Non-Intrusive Reduced-Order Model Developed for Parameterized Time-Dependent Problems[J]. Northwestern polytechnical university |
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| 一种针对带参数非定常问题的非嵌入式降阶模型 |
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| 王晨1, 白俊强1, Jan S Hesthaven2, 邱亚松1, 杨体浩1 |
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1. 西北工业大学 航空学院, 陕西 西安 710072;
2. 洛桑联邦理工(EPFL), 瑞士 洛桑 CH-1015 |
| 摘要: |
| 对于带参数问题的非线性系统，采用基于本征正交分解方法（POD）的2层本征正交分解方法（two-level POD）提取系统的空间、时间特征模态，再利用最小二乘法配合径向基函数（RBF）法预测模态的投影系数，建立了一种预测过程不依赖于系统所用控制方程的非嵌入式降阶模型。为了降低径向基函数法对核函数中经验参数的依赖和提高数值稳定性，用引入QR变换等数学手段构造的RBF-QR取代标准RBF方法来预测拟合系数。在一维Burgers方程和驱动腔内流算例中，此非嵌入式降阶模型在获得适当的快照数据后，能精确快速地预测和复现参数域内任一点的非定常流场。 |
| 关键词:
非嵌入
2层POD
径向基函数
QR分解
驱动腔
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| A Non-Intrusive Reduced-Order Model Developed for Parameterized Time-Dependent Problems |
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| Wang Chen1, Bai Junqiang1, Jan S Hesthaven2, Qiu Yasong1, Yang Tihao1 |
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1. School of Aeronautics, Northwestern Polytechnical University, Xi'an 710072, China;
2. Swiss Federal Institute of Technology in Lausanne(EPFL), CH-1015 Lausanne, Switzerland |
| Abstract: |
| For parameterized time-dependent problems, we propose to adopt two-level proper decomposition to extract temporal and spatial basis functions and radial basis function(RBF) model to be used to approximate the undetermined coefficients, thus forming a non-intrusive reduced order method(ROM), of which the approximation process doesn't rely on the governing equation after reduced basis obtained. In order to reduce the dependence of RBF on empirical parameters, a new RBF which exerts QR decomposition and other mathematical approaches on the standard RBF is used in our proposed ROM. When approximating one-dimensional Burgers equation and a driven cavity problem governed by incompressible Navier-Stokes equations, results show that the non-intrusive ROM predicts the unsteady flow field fast and accurately at any point in the parameter domain. |
| Key words:
non-intrusive
two-level POD
radial Basis Function
QR decomposition
driven cavity
computational efficiency
Mesh generation
parameterization
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| 收稿日期: 2017-03-01
修回日期:
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| DOI: |
| 基金项目: 国家自然科学基金（11602199）资助 |
| 通讯作者:
Email： |
| 作者简介: 王晨(1989-),西北工业大学博士研究生,主要从事降阶模型及计算流体力学研究。
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