|
|
论文:2019,Vol:37,Issue(1):70-79 |
|
|
引用本文： |
|
|
孟俊男, 潘光, 曹永辉, 李林丰, 黎针岑, 周冰. 基于无网格伽辽金法的非线性流动数值模拟[J]. 西北工业大学学报 |
|
|
MENG Junnan, PAN Guang, CAO Yonghui, LI Linfeng, LI Zhencen, ZHOU Bing. Numerical Simulation of Nonlinear Flow Based on Element-Free Galerkin Method[J]. Northwestern polytechnical university |
|
|
|
|
|
|
|
| 基于无网格伽辽金法的非线性流动数值模拟 |
|
| 孟俊男, 潘光, 曹永辉, 李林丰, 黎针岑, 周冰 |
|
| 西北工业大学 航海学院 西北工业大学无人水下运载技术重点实验室, 陕西 西安 710072 |
| 摘要: |
| 基于无网格伽辽金方法针对典型的非线性流动问题进行数值研究，对Navier-Stokes方程使用Galerkin方法离散，方程中的惯性项分别采取速度项提出法和直接推导法进行离散，使用罚函数法施加压力和速度边界条件，建立了基于EFG法的二维N-S方程的离散形式。针对定常非线性流动问题，对矩形域上下平板相向运动流动进行数值模拟，结果表明该方法求解精度比较高，计算误差不超过3.66%；针对非定常非线性流动问题，采取θ加权法对N-S方程中的时间项进行离散，建立了EFG法非定常求解方程。以方柱绕流问题为例，证明了文中所建立的非定常算法的精度及收敛性。 |
| 关键词:
无网格伽辽金法
罚函数法
Navier-Stokes方程
直接线性交替迭代法
|
|
| Numerical Simulation of Nonlinear Flow Based on Element-Free Galerkin Method |
|
| MENG Junnan, PAN Guang, CAO Yonghui, LI Linfeng, LI Zhencen, ZHOU Bing |
|
| Key Laboratory for Unmanned Underwater Vehicle, School of Marine Science and Technology, Northwestern Polytechnical University, Xi'an 710072, China |
| Abstract: |
| This paper focuses on the studying on some flow problems of nonlinear based on the Element Free Galerkin method. First the Navier-Stokes equation is discretized with the Galerkin method. The inertial term in the equation is discretized with the method of the speed term and direct deduction respectively. And the penalty function method is used to deal with the pressure and the essential boundary condition in the equation, and the discretization of two-dimensional N-S equation based on the EFG method is established. Then the flow problem of stationary nonlinear is studied. The flow problem of water in the rectangular domain squeezed by the two plates distributed above and below the calculated domain is studied with the method of EFG. The accuracy of the direct linear alternating interation method is shown by contrast with the analytical solution. Then the flow problem of unsteady nonlinear is studied. The θ-weighted method is used to discrete the time term of the N-S equation and the unsteady nonlinear solution matrix of EFG is established. The flow problem of flow around the square column is studied with the method of EFG and the flows under a series of low Reynolds are stimulated. |
| Key words:
element-free Galerkin method
penalty function method
Navier-Stokes equation
direct linear alternating interation method
|
|
| 收稿日期: 2018-03-12
修回日期:
|
| DOI: 10.1051/jnwpu/20193710070 |
| 基金项目: 国家重点研发计划（2016YFC0301300）与国家自然科学基金（11502210，51709229，5149170）资助 |
| 通讯作者: 潘光(1969-),西北工业大学教授、博士生导师,主从事水中兵器总体设计及流体力学研究。E-mail:panguang@nwpu.edu.cn
Email：panguang@nwpu.edu.cn |
| 作者简介: 孟俊男(1993-),女,西北工业大学博士研究生,主要从事扑翼推进机理研究。
|
|
| 相关功能 |
|
|
|
|
| 作者相关文章 |
|
| 孟俊男 在本刊中的所有文章 |
| 潘光 在本刊中的所有文章 |
| 曹永辉 在本刊中的所有文章 |
| 李林丰 在本刊中的所有文章 |
| 黎针岑 在本刊中的所有文章 |
| 周冰 在本刊中的所有文章 |
|
|
|
|
|
|
|
|
参考文献: |
|
|
[1] 蒋博,蔡晓龙. 基于Matlab的移动最小二乘法数据拟合[J]. 数学技术与应用,2015(10):110-111 JIANG Bo, CAI Xiaolong. Matlab-Based Mobile Least Squares Data Fitting[J]. Mathematical Technology and Applications, 2015(10):110-111 (in Chinese)
[2] 吴俊超,邓俊俊,王家睿. 伽辽金型无网格法的数值积分方法[J]. 固体力学学报,2016,37(3):208-233 WU Junchao, DENG Junjun, WANG Jiarui. Galerkin-Type Meshless Numerical Integration Method[J]. Chinese Journal of Solid Mechanics, 2016, 37(3):208-233 (in Chinese)
[3] 丁睿,朱征城. 一类时间二阶发展型变分不等式的EFG方法及其收敛性分析[J]. 应用数学学报,2015,38(5):874-891 DING Rui, ZHU Zhengcheng. The EFG Method and Its Convergence Analysis for a Class of Time-Order Second-Order Variational Inequalities[J]. Chinese Journal of Applied Mathematics, 2015, 38(5):874-891 (in Chinese)
[4] LUCY L B. A Numerical Approach to the Testing of the Fission Hypothesis[J]. The Astronomical Journal, 1977, 82(12):1013-1024
[5] JOHNSON G R, BEISSEL S R. Normalized Smoothing Functions for Sph Impact Computations[J]. International Journal for Numerical Methods in Engineering, 1996, 39:2725-2741
[6] LANCASTER P, SALKAUSKAS K. Surfaces Generated by Moving Least Squares Methods[J]. Mathematics of Computation, 1981, 37:141-158
[7] PITA C M, FELICELLI S D. Applications of the Immersed Element-Free Galerkin Method[J]. Mecnica Computacional, 2008(8):541-561
[8] 杨建军,郑建龙. 无网格局部强弱法求解不规则域问题[J]. 力学学报,2017,49(3):659-666 YANG Jianjun, ZHENG Jianlong. The Meshless Local Strong and Weak Method Solves the Irregular Domain Problem[J]. Chinese Journal of Mechanics, 2017, 49(3):659-666 (in Chinese)
[9] SHEDBALE A S, SINGH I V. Ductile Failure Modeling and Simulations Using Coupled Fe-EFG Approach[J]. International Journal of Fracture,2016,203(1/2):183-209
[10] 张飞,张国达,任红萍. 基函数的阶数对无单元伽辽金方法精度的影响[J]. 西南民族大学学报,2017,43(2):177-185 ZHANG Fei, ZHANG Guoda, REN Hongping. The Influence of the Order of Basis Functions on the Accuracy of the Elementless Galerkin Method[J]. Journal of Southwest University for Nationalities, 2017, 43(2):177-185 (in Chinese)
[11] 易若愚. 二维N-S方程的EFG数值模拟及其应用研究[D]. 湘潭:湘潭大学,2016 YI Ruoyu. Efg Numerical Simulation of Two-Dimensional N-S Equations and Its Application[D]. Xiangtan, Xiangtan University, 2016 (in Chinese)
[12] 欧阳邦,龚曙光. EFG法二维不可压缩层流问题的数值方法研究[D]. 湘潭:湘潭大学,2016 OUYANG Bang, GONG Shuguang. Numerical Method for Two-Dimensional Incompressible Laminar Flow Problem with EFG Method[D]. Xiangtan, Xiangtan University, 2016 (in Chinese)
[13] MICHAEL Hillman, CHEN Jiunshyan. An Accelerated, Convergent, and Stable Nodal Integration in Galerkin Meshfree Methods for Linear and Nonlinear Mechanics[J]. International Journal for Numerical Methods in Engineering, 2016, 107:603-630
[14] 覃霞,曾治平,彭林欣. 弹性地基上矩形加肋板自由振动分析的无网格法[J]. 应用力学学报,2017,34(6):1027-1033 QIN Xia, ZENG Zhiping, PENG Linxin. Free Mesh Vibration Analysis of Rectangular Ribbed Plates on Elastic Foundations[J]. Chinese Journal of Applied Mechanics, 2017, 34(6):1027-1033 (in Chinese)
[15] LI Xiaolin. A Meshless Interpolating Galerkin Boundary Node Method for Stokes Flows[J]. Engineering Analysis with Boundary Elements,2015,51:112-122
[16] FAYSSAL B, HALASSI A, DRISS O, et al. A Stabilized Meshless Method for Time-Dependent Convection-Dominated Flow Problems[J]. Mathematics and Computers in Simulation, 2017, 137:159-176
[17] 陈苍,杨书仪. 冲击动力学中无网格法应用[J]. 湖南大学学报,2017, 32(1):30-36 CHEN Cang, YANG Shuyi. Application of Meshless Method in Impact Dynamics[J]. Journal of Hunan University, 2017, 32(1):30-36 (in Chinese)
[18] 程玉民. 无网格方法[M]. 北京:科学出版社, 2015 CHENG Yumin. Meshless Method[M]. Beijing, Science Press, 2015 (in Chinese) |
|
|
|
|
|
|
|
