Abstract: Background-oriented schlieren (BOS) is an important non-contact method for measuring flow density field. The den
sity field is typically calculated by solving the Poisson equation using finite difference methods. However, the current methods for
calculating the Poisson equation source term (i.e., the first-order derivatives of ray deflection angles at grid nodes) are time-con
suming and low accuracy where deflection angles change hardly. To address these issues, a hash function is created to establish a
mapping between point coordinates and the deflection angles by this paper based on ray deflection angles measured by BOS, to
find rapidly the BOS measurement point set and their deflection angles within a local region whose center is the given point. A
method is developed to capture measurement points where deflection angles change hardly, used to divide the field into regions
accordingly, and the interpolation-based derivative formula is derived to calculate the deflection angles’ derivatives within these
regions. The simulation experiments demonstrate the proposed method reduces the residuals by 56.66% and peak error by 75.8%,
compared to existing methods for calculating the source term of the Poisson equation, have the better results at peaks of density
changing. The wind tunnel experiments further demonstrate this method achieves a better refinement density field of a cavity
model with significant speed-up computing ratio up to 3582.72, compared to existing approaches. The measuring results of the
weak shock wave at the head of the " 7°(semi-apex angle)cone-cylinder model and a sonic boom model" in the 2-meter supersonic
wind tunnel are consistent with the theoretical values, and the maximum relative error of the density ratio on both sides of this
weak shock wave is 3.9%, and the flow field density reconstruction is correct. Therefore, this method improves the rate, accuracy
and weak shock wave capture ability for BOS measuring density field, and has great engineering application value.
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