Non-linear Petrov-Galerkin methods for reduced order modelling of the Navier-Stokes equations using a mixed finite element pair
Non-linear Petrov-Galerkin methods for reduced order modelling of the Navier-Stokes equations using a mixed finite element pair
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DOI：
10.1016/j.cma.2012.11.002
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发表时间：
2013-03
影响因子：
7.2
通讯作者：
D. Xiao;F. Fang;Juan Du;C. Pain;Ionel M. Navon;A. Buchan;A. Elsheikh;G. Hu
中科院分区：
文献类型：
--
作者：
D. Xiao;F. Fang;Juan Du;C. Pain;Ionel M. Navon;A. Buchan;A. Elsheikh;G. Hu
发展了一种新的非线性Petrov-Galerkin方法，用于对Navier-Stokes方程进行本征正交分解(POD)降阶建模。新方法基于笛卡尔时空中平流方向与解的梯度方向之间的余弦规则。这里使用的有限元对P1DGP2具有良好的保平衡性能，它由不连续(速度分量)和连续(压力分量)基函数组成。本文的贡献在于将这种新的非线性Petrov-Galerkin方法应用于降阶的Navier-Stokes方程，从而在不调整参数的情况下提高了ROM解的稳定性。给出了用非结构网格有限元CFD模型模拟的风致二维旋涡和圆柱绕流的数值试验结果，以说明该方法的数值性能。数值结果表明，新提出的POD-Petrov-Galerkin方法比POD-Bubnov-Galerkin方法具有更高的精度和稳定性。
A new nonlinear Petrov–Galerkin approach has been developed for proper orthogonal decomposition (POD) reduced order modelling (ROM) of the Navier–Stokes equations. The new method is based on the use of the cosine rule between the advection direction in Cartesian space–time and the direction of the gradient of the solution. A finite element pair, P1DGP2, which has good balance preserving properties is used here, consisting of a mix of discontinuous (for velocity components) and continuous (for pressure) basis functions. The contribution of the present paper lies in applying this new non-linear Petrov–Galerkin method to the reduced order Navier–Stokes equations, and thus improving the stability of ROM results without tuning parameters. The results of numerical tests are presented for a wind driven 2D gyre and the flow past a cylinder, which are simulated using the unstructured mesh finite element CFD model in order to illustrate the numerical performance of the method. The numerical results obtained show that the newly proposed POD Petrov–Galerkin method can provide more accurate and stable results than the POD Bubnov–Galerkin method.