ACTA AERONAUTICAET ASTRONAUTICA SINICA >
Fast calculation method of Poisson equation source term for BOS measuring density field
Received date: 2024-12-25
Revised date: 2025-01-13
Accepted date: 2025-02-10
Online published: 2025-02-27
Supported by
National Natural Science Foundation of China(11872069)
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.
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 AERONAUTICAET ASTRONAUTICA SINICA, 2025 , 46(17) : 131713 -131713 . DOI: 10.7527/S100-6893.2025.31713
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