A computational fluid dynamic method is developed to calculate the long range propagation of weak shock wave with the vibrational relaxation in air. Vibrational relaxation kinetics among N2, O2, and H2O is accounted for by solving each species conservation equations with total mass, momentum and energy equations. The conservation equations are solved using a moving grid technique to capture the distortion of the wave during propagation. The propagation of the wave with an overpressure value typically observed in sonic boom on the ground is analyzed using the developed method. The computed results are mainly presented to show the ability to capture a dispersed nature in waves under different humidity conditions due to vibrational relaxation. The present result shows that the variation of a converged wave thickness dependent on a wide range of humidity can be recognized clearly by using the present method.

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