自由节点差分法寻点策略研究及验证

卢俊宇; 徐春光; 陈洁; 刘君; 王元靖

doi:10.7638/kqdlxxb-2023.0015

欢迎来到能源电力期刊网！

English Version 期刊登录

您当前的位置：

首页 >

文章列表页 >

自由节点差分法寻点策略研究及验证

研究论文 | 更新时间：2026-05-28

- 自由节点差分法寻点策略研究及验证
- Research and verification of point selection strategy for flexible-node finite difference method
- 空气动力学学报 2024年42卷第4期页码：65-74
- 作者机构：
  
  1. 中山大学航空航天学院,广州,510275
  2. 大连理工大学航空航天学院,大连,116024
  3. 宁波大学机械工程与力学学院,宁波,315211
  4. 中国空气动力研究与发展中心高速空气动力研究所,绵阳,621000
- 作者简介：
  
  卢俊宇（1998—），男，广东人，硕士研究生，研究方向：CFD计算方法及应用. E-mail：863964629@qq.com
  徐春光*，副教授，研究方向：CFD计算方法及应用. E-mai：xuchg5@mail.sysu.edu.cn
  王元靖*，研究员，研究方向：飞行器气动设计与优化. E-mail：wyjnan@163.com
- 基金信息：
- DOI：10.7638/kqdlxxb-2023.0015
  中图分类号： V211.3
- 纸质出版：2024
- 稿件说明：
移动端阅览
卢俊宇, 徐春光, 陈洁, 等. 自由节点差分法寻点策略研究及验证[J]. 空气动力学学报, 2024, 42(4): 65−74.

LU Junyu, XU Chunguang, CHEN Jie, et al. Research and verification of point selection strategy for flexible-node finite difference method[J]. 2024, 42(4): 65-74.
卢俊宇, 徐春光, 陈洁, 等. 自由节点差分法寻点策略研究及验证[J]. 空气动力学学报, 2024, 42(4): 65−74. DOI： 10.7638/kqdlxxb-2023.0015

LU Junyu, XU Chunguang, CHEN Jie, et al. Research and verification of point selection strategy for flexible-node finite difference method[J]. 2024, 42(4): 65-74. DOI： 10.7638/kqdlxxb-2023.0015.

摘要

混合网格具有良好的贴体性，适用于Navier-Stokes方程的计算，但在网格交界面处需要通过插值进行流场信息交换，而这一过程会引入误差。陈洁等提出了一种适用于无序网格点的自由节点差分计算方法，该方法可对重叠网格交界面流场进行差分计算，无须采用插值方法进行流场信息传递，解决了插值方法引入误差的问题。但该自由节点差分法的计算模板需要从中心点周围的点云中选择网格点构成，不同选点策略对计算结果的影响不同。针对自由节点差分法的选点需求，本文综合考虑角度、正交性、距离等因素，提出了几种不同选点策略，并利用数值实验进行了验证。结果表明，本文提出的选点策略符合自由节点差分法的构造思想，均能获得稳定的收敛解，其中模板点与中心点距离对计算精度影响最大，是选点策略的首要影响因素。

Abstract

Hybrid grid is usually composed of spatial cartesian grid and body-fitted grid

which combine the advantages of cartesian grid and body-fitted grid

and has certain advantages in the grid generation and processing of complex geometries shapes. It has become an important grid generation technique in CFD. In the hybrid grid

there is an interface between the spatial cartesian grid and the body-fitted grid

and the flow field information between them needs to be exchanged by interpolation. This process will introduce extra errors and affect the calculation accuracy of the flow field. To solve this problem

Chen et al. proposed flexible-node difference method (FN-FDM) based on DEER algorithm

which can conduct the difference computation of overlapping grid interface flow field and reduce the errors introduced by interpolation computation. The computation stencil of FN-FDM needs to select the grid points from the point cloud around the central point

and different point selection strategies have different effects on the calculation results. Aiming at the point selection requirement of FN-FDM

this paper proposes several different point selection strategies considering angle

orthogonality

distance and other factors

and verifies them by numerical experiments. Numerical experimental results show that the proposed point selection strategy based on the construction idea of FN-FDM

can obtain stable convergence solutions. The distance between the computation point and the central point has the most prominent influence on the computational accuracy

and is the major influence factor of the point selection strategy.

关键词

Keywords

references

YAN C, QU F, ZHAO Y T, et al . Review of development and challenges for physical modeling and numerical scheme of CFD i n aeronautics and astronautics[J ] . Acta Aerodynamica Sinica, 2020 , 38 ( 5 ): 829 − 857 (in Chinese).

YAN C. Computational fluid dynamics method and its application[M]. Beijing: Beijing University of Aeronautics and Astronautics Press, 2006 (in Chinese).

SLOTNICK J , KHODADOUST A , ALONSO J , et al. CFD vision 2030 study: A path to revolutionary computational aerosciences, NF1676L-18332[R]. Hampton, Virginia: NASA langley research center, 2014.

JAMESON A, YOON S . Lower-upper implicit schemes with multiple grids for the Euler equations[J ] . AIAA Journal, 1987 , 25 ( 7 ): 929 − 935 .

BATTEN P, LESCHZINER M A . GOLDBERG U C. Average-state jacobians and implicit methods for compressible viscous and turbulent flows[J ] . Journal of Computational Physics, 1997 , 137 ( 1 ): 38 − 78 .

MARCUM D. Generation of unstructured grids for viscous flow applications[C]// 33rd Aerospace Sciences Meeting and Exhibit, Reno, NV, USA. Reston, Virigina: AIAA, 1995.

LUO H, BAUM J D . A fast, matrix-free implicit method for compressible flows on unstructured grids[J ] . Journal of Computational Physics, 1998 , 146 ( 2 ): 664 − 690 .

CLARKE D K, SALAS M D, HASSAN H A . Euler calculations for multielement airfoils using Cartesian grids[J ] . AIAA Journal, 1986 , 24 ( 3 ): 353 − 358 .

DELANAYE M, AFTOSMIS M, BERGER M, et al. Automatic hybrid-Cartesian grid generation for high-Reynolds number flows around complex geometries[C]// 37th Aerospace Sciences Meeting and Exhibit, Reno, NV, USA. Reston, Virigina: AIAA, 1999.

SONG Z F, ZHAO N, SHEN Z W, et al . Hybrid Cartesian grid method for compressible viscous flows[J ] . Aeronautical Computing Technique, 2014 , 44 ( 1 ): 37 − 40,44 (in Chinese).

IACCARINO G, VERZICCO R . Immersed boundary technique for turbulent flow simulations[J ] . Applied Mechanics Reviews, 2003 , 56 ( 3 ): 331 − 347 .

WANG J Y, SHAN P, ZHU H T . Immersed body-fitted meshes boundary method[J ] . Journal of Aerospace Power, 2021 , 36 ( 4 ): 713 − 723 (in Chinese).

LIU J M, ZHAO N, HU O, et al . A new immersed boundary method for compressible Navier-Stokes equations[J ] . International Journal of Computational Fluid Dynamics, 2013 , 27 ( 3 ): 151 − 163 .

LIU J, WEI Y X, HAN F . Coordinate transformation induced errors of finite difference method[J ] . Acta Aeronautica et Astronautica Sinica, 2021 , 42 ( 6 ): 343 − 358 (in Chinese).

HUANG Y, YAN C, WANG W, et al . An improved interpolation method for hybrid overset grid and its application[J ] . Journal of Beijing University of Aeronautics and Astronautics, 2017 , 43 ( 2 ): 285 − 292 (in Chinese).

HONG Z C, ZONG Z, WANG Y G, et al . Research on uncertainty of overset mesh tec hnology based on orthogonal experiment method[J ] . Journal of Ship Mechanics, 2020 , 24 ( 7 ): 865 − 873 (in Chinese).

CHEN J, WANG J S, LU J Y. Research progress of viscous flow automated CFD calculation technology[J]. Aerospace Technology, 2024: 1-20 (in Chinese).

LIU J, CHEN J, HAN F . Finite difference method for unstructured grid based on discrete equivalent equation[J ] . Acta Aeronautica et Astronautica Sinica, 2020 , 41 ( 1 ): 119 − 128 (in Chinese).

LIU J, HAN F, XIA B . Mechanism and algorithm for geometric conservation law in finite difference method[J ] . Acta Aerodynamica Sinica, 2018 , 36 ( 6 ): 917 − 926 (in Chinese).

LI X L, REN Y X, LI W . Construction of the high order accurate generalized finite difference schemes for inviscid compressible flows[J ] . Communications in Computational Physics, 2019 , 25 ( 2 ): 481 − 507 .

LUCY L B . A numerical approach to the testing of the fission hypothesis[J ] . The Astronomical Journal, 1977 , 82 : 1013 − 1024 .

GINGOLD R A, MONAGHAN J J . The collapse of a rotating non-axisymmetric isothermal cloud[J ] . Monthly Notices of the Royal Astronomical Society, 1981 , 197 ( 2 ): 461 − 475 .

NAYROLES B, TOUZOT G, VILLON P . Generalizing the finite element method: Diffuse approximation and diffuse elements[J ] . Computational Mechanics, 1992 , 10 ( 5 ): 307 − 318 .

BELYTSCHKO T, LU Y Y, GU L . Element-free Galerkin methods[J ] . International Journal for Numerical Methods in Engineering, 1994 , 37 ( 2 ): 229 − 256 .

JIANG Y, SHU C W, ZHANG M P . Free-stream preserving finite difference schemes on curvilinear meshes[J ] . Methods and Applications of Analysis, 2014 , 21 ( 1 ): 1 − 30 .

NONOMURA T, TERAKADO D, ABE Y, et al . A new technique for freestream preservation of finite-difference WENO on curvilinear grid[J ] . Computers Fluids, 2015 , 107 : 242 − 255 .

ZHU Y J, SUN Z S, REN Y X, et al . A numerical strategy for freestream preservation of the high order weighted essentially non-oscillatory schemes on stationary curvilinear grids[J ] . Journal of Scientific Computing, 2017 , 72 ( 3 ): 1021 − 1048 .

Guan T N, Chen J, Xu C G, et al . A second-order-accuracy finite difference scheme for numerical computation on two-dimensional three-neighboring-node unstructured grids[J ] . Physics of Fluids, 2024 , 36 : 036109 .

浏览量

下载量

CSCD

文章被引用时，请邮件提醒。

提交

工具集

关联资源

大展弦比飞行器突风响应数值计算

某型电动跑车尾翼气动设计的仿真与试验研究

离心通风机降噪研究进展

交错型CPR方法的保正实现策略及其对比研究

基于LBM方法的LAGOON起落架噪声预测与降噪方法研究