Non-linear model reduction for the Navier-Stokes equations using residual DEIM method
Non-linear model reduction for the Navier-Stokes equations using residual DEIM method
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DOI：
10.1016/j.jcp.2014.01.011
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发表时间：
2014-04
期刊：
影响因子：
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通讯作者：
D. Xiao;F. Fang;A. Buchan;C. Pain;Ionel M. Navon;Juan Du;G. Hu
中科院分区：
文献类型：
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作者：
D. Xiao;F. Fang;A. Buchan;C. Pain;Ionel M. Navon;Juan Du;G. Hu
本文提出了一种基于本征正交分解（POD）的求解Navier-Stokes方程的降阶模型。该方法的新奇在于它的治疗方程的非线性算子，提出了一种新的方法，提供准确的模拟在一个有效的框架。该方法本身是一个混合的两个现有的方法，即二次展开法和离散经验插值法（DEIM），已经开发的降阶模型内处理非线性算子。提出的方法应用二次展开提供一个第一近似的非线性算子，和DEIM然后被用来作为一个校正，以改善其表示。除了处理的非线性算子的POD模型稳定使用Petrov-Galerkin方法。通过求解不可压Navier-Stokes方程模拟圆柱绕流和涡旋问题，验证了该方法的有效性.与其他处理的非线性算子的比较，这些表明新的方法，以提供显着的改善解决方案的精度。
This article presents a new reduced order model based upon proper orthogonal decomposition (POD) for solving the Navier–Stokes equations. The novelty of the method lies in its treatment of the equation's non-linear operator, for which a new method is proposed that provides accurate simulations within an efficient framework. The method itself is a hybrid of two existing approaches, namely the quadratic expansion method and the Discrete Empirical Interpolation Method (DEIM), that have already been developed to treat non-linear operators within reduced order models. The method proposed applies the quadratic expansion to provide a first approximation of the non-linear operator, and DEIM is then used as a corrector to improve its representation. In addition to the treatment of the non-linear operator the POD model is stabilized using a Petrov–Galerkin method. This adds artificial dissipation to the solution of the reduced order model which is necessary to avoid spurious oscillations and unstable solutions.A demonstration of the capabilities of this new approach is provided by solving the incompressible Navier–Stokes equations for simulating a flow past a cylinder and gyre problems. Comparisons are made with other treatments of non-linear operators, and these show the new method to provide significant improvements in the solution's accuracy.