Accurate and efficient wall distance calculation method for Cartesian grids

MENG Shuang; ZHOU Dan; LI Xueliang; BI Lin

doi:10.7638/kqdlxxb-2021.0359

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Accurate and efficient wall distance calculation method for Cartesian grids

更新时间：2026-05-28

- Accurate and efficient wall distance calculation method for Cartesian grids
- Vol. 41, Issue 7, Pages: 93-101(2023)
- 作者机构：
  
  1. 中南大学轨道交通安全教育部重点实验室,长沙,410075
  2. 空气动力学国家重点实验室,绵阳,621000
  3. 中国空气动力研究与发展中心计算空气动力研究所,绵阳,621000
- 作者简介：
- 基金信息：
- DOI：10.7638/kqdlxxb-2021.0359
  CLC： V211.3
- Published：2023
- 稿件说明：
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孟爽, 周丹, 李雪亮, 等. 笛卡尔网格下精确高效的壁面距离计算方法[J]. 空气动力学学报, 2023, 41(7): 93−101.

MENG Shuang, ZHOU Dan, LI Xueliang, et al. Accurate and efficient wall distance calculation method for Cartesian grids[J]. 2023, 41(7): 93-101.
孟爽, 周丹, 李雪亮, 等. 笛卡尔网格下精确高效的壁面距离计算方法[J]. 空气动力学学报, 2023, 41(7): 93−101. DOI： 10.7638/kqdlxxb-2021.0359

MENG Shuang, ZHOU Dan, LI Xueliang, et al. Accurate and efficient wall distance calculation method for Cartesian grids[J]. 2023, 41(7): 93-101. DOI： 10.7638/kqdlxxb-2021.0359.

摘要

对于笛卡尔网格方法，壁面距离是采用虚拟单元法精确处理物面边界的重要参数，同时也是网格自适应后制约流动计算效率的关键因素之一。针对现有壁面距离计算方法结果不精确、效率不高的问题，引入三角形参数化方法，将空间点到三角形物面离散网格的最小距离问题转换为约束条件下一维极值问题，仅需通过符号判断和少量加减乘运算，即可确定最小距离，计算精度和效率大幅提高；发展嵌套包围盒概念的KDT（K-dimensional tree）物面网格数据存储结构，优化KDT最近邻搜索算法中距物面较远数据点回溯过程，实现了最小距离对应的三角形的快速定位。运用球、导弹、DPW6等三维几何构型对上述方法考核验证结果表明，计算得到的壁面距离与解析值的误差在百万分之一以内，十亿量级网格规模下的单核计算效率接近已有文献中的并行计算效率。

Abstract

The wall distance of Cartesian grids is an essential parameter for the proper wall treatment using ghost cells and is also one of the critical factors governing the efficiency of the flow field simulation after mesh adaptation. This paper proposes a triangular parameterization method that converts the problem of computing the minimum distance between spatial points and discretized triangular meshes on the surface into a constrained one-dimensional extremum problem. This simplification only requires symbolic judgments and a small number of addition

subtraction and multiplication operations to obtain the minimal distance

yielding significant improvements in the accuracy and efficiency compared to existing methods. Meanwhile

a KDT (K-dimensional tree) data structure based on the nested enclosing box concept is developed to optimize the backtracking of data points far from the surface in the KDT nearest neighbor search algorithm. The application of this method to three-dimensional geometries such as spheres

missiles

and DPW6 demonstrates that the error between the computed wall distance and the resolved one is within one millionth. Moreover

the computational costs of using a single core for billion-scale grids are comparable to those of parallel computation using existing methods.

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Keywords

references

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