瞬态Navier-Stokes方程的最小二乘有限元降阶计算方法

发布时间：2018-03-04 00:34

本文选题：Navier-Stokes方程　切入点：降阶模型　出处：《华北电力大学学报(自然科学版)》2017年03期 　论文类型：期刊论文

【摘要】：为了解决在应用数值算法计算瞬态流体方程以分析流体运动特征时,方程的自由度过大,所耗用计算资源较多的问题,提出了一种求解瞬态不可压缩流体问题的降阶计算方法。该方法首先应用最小二乘有限元法计算部分时刻流场的解构成瞬像矩阵,然后对瞬像矩阵进行特征正交分解(Proper Orthogonal Decomposition,POD)提取流场的特征函数,最后结合Galerkin正交投影方法构建求解瞬态Navier-Stokes方程的降阶计算模型。应用降阶计算方法对顶盖驱动流模型进行分析,计算结果表明:前9阶POD正交基可以捕获流场超过99%的广义能量信息,能够比较精确地描述流场的主要物理特征,所构造的降阶模型方程的自由度远小于全阶模型方程的自由度;降阶模型的计算结果与全阶模型的计算结果符合得很好,验证了降阶计算方法的准确性。
[Abstract]:In order to solve the problem that the degree of freedom of the equation is too large and the computational resources are much more when the numerical algorithm is used to calculate the transient fluid equation to analyze the characteristics of fluid motion, In this paper, a reduced order method for solving transient incompressible fluid problems is proposed. Firstly, the solution of partial flow field is calculated by using the least square finite element method to form the instantaneous image matrix. Then the characteristic function of the flow field is extracted from the instantaneous image matrix by using the characteristic orthogonal decomposition Proper Orthogonal decomposition POD. Finally, the reduced order calculation model for the transient Navier-Stokes equation is constructed by using the Galerkin orthogonal projection method. The reduced order calculation method is used to analyze the driving flow model of the roof. The results show that the first 9 order POD orthogonal basis can capture the generalized energy information of the flow field over 99%, and can accurately describe the main physical characteristics of the flow field. The degree of freedom of the reduced model equation is much smaller than that of the full-order model equation, and the calculation results of the reduced model are in good agreement with that of the full-order model, which verifies the accuracy of the reduced-order calculation method.
【作者单位】：华北电力大学新能源电力系统国家重点实验室;
【基金】：国家自然科学基金资助项目(51277064)
【分类号】：O241.82

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