Research and verification of point selection strategy for flexible-node finite difference method

LU Junyu; XU Chunguang; CHEN Jie; LIU Jun; WANG Yuanjing

doi:10.7638/kqdlxxb-2023.0015

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Research and verification of point selection strategy for flexible-node finite difference method

更新时间：2026-05-28

- Research and verification of point selection strategy for flexible-node finite difference method
- Vol. 42, Issue 4, Pages: 65-74(2024)
- 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：
- 基金信息：
- DOI：10.7638/kqdlxxb-2023.0015
  CLC： V211.3
- Published：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

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references

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