A comparative study of CCW and Milton’s methods: on the strong shock waves in van der waals gas flow through a variable cross-section area

Abstract This paper presents a significant study on the behavior of a strong shock wave in a real gas traveling through a channel with a small change in cross-sectional area using the van der Waals equation of state. The study provides detailed comparisons of the shock behavior with varying cross-sectional areas using the CCW and Milton’s methods. The analytical solutions of the flow variable for perturbed shocks are calculated, considering the overtaking disturbances arising from the contact discontinuity. The findings explain how the varying area and overtaking disturbances influence the pattern of the shock velocity, particle velocity, pressure, and density. The flow variables increase rapidly with the non-idealness parameter and the adiabatic index of the gas up to their peak point and then decrease gradually. The variations of the shock velocity, particle velocity, pressure, and density under both methods have been explained in graphical and tabular forms. The range of the flow variables gets strengthened two to four times with the inclusion of the reflected and re-reflected disturbances in Milton’s method. The findings are in complete agreement with the existing results, and the study significantly contributes to the various branches of fluid dynamics.