BOS测量密度场泊松方程源项快速计算方法

doi:10.7527/S100-6893.2025.31713

Abstract

Abstract:

Background-Oriented Schlieren （BOS） is a vital non-intrusive method for measuring fluid density field. The finite difference method is employed to solve the Poisson equation for calculating the projected density field. However， existing approaches for computing the source term of the Poisson equation （which mainly includes the first-order partial derivatives of the light deflection angle at the grid nodes） are time-consuming and poor precision at discontinuities with abrupt changes. To address this issue， a fast calculation method of Poisson equation source term for BOS measuring density field is proposed. A Hash function between the point coordinates and the light deflection angle field data is presented to rapidly locate the BOS measurement points， their deflection angles in a local area centered around a given point， and the interpolation-based derivative formula for this local area are constructed. A region division method is proposed for areas with abrupt changes in light deflection angle， where first-order partial derivatives are computed separately using Hash tables and local interpolation. Simulation results show a 56.66% reduction in residuals and a 75.8% decrease in peak error near abrupt changes. For a cavity wind tunnel model， the method yields a finer density field and achieves a 411.85 speedup over existing Poisson source term methods. Two supersonic wind tunnel tests， on a 7° cone-cylinder and a sonic boom model， validate the method， with weak head shock waves closely matching theory and a maximum density ratio error of only 3.9%. The method proposed in this paper therefore improves the rapid and accuracy of the density field measurement， and can capture weak shock waves， offering substantial application value.

Key words: density field reconstruction, light deflection angle, background-oriented schlieren, Poisson equation, Hash function

CLC Number:

V556.5

Jian ZHANG, Zhengyu ZHANG, Yang YANG, Fengxue QIAN, Xiaoxia LI, Caigang WANG, Jiajie LUO. Fast calculation method of Poisson equation source term for BOS measuring density field[J]. Acta Aeronautica et Astronautica Sinica, 2025, 46(17): 131713.

Figures/Tables 21

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查找算法	算法复杂度
遍历查找	O（m×n）
算法1^［25］	O（m+n）
本文算法	O（1）

网格尺寸	耗时/ms		加速比
网格尺寸	传统方法^［27］	本文方法	加速比
100×100	13 481	47	286.83
150×150	29 802	73	408.25
200×200	56 334	101	557.76

参数	方法	数值
网格大小		249×108
耗时/ms	文献［27］	44 892
耗时/ms	本文方法	109
加速比		411.85

Fast calculation method of Poisson equation source term for BOS measuring density field

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