On the modified dispersion-controlled dissipative (DCD) scheme for computation of flow supercavitation

In the present study, a robust scheme initially proposed for capturing shock waves in gasdynamics, the dispersion-controlled dissipative (DCD) scheme is modified to simulate supercavitating flows in the framework of one-fluid model. Due to the stiffness of the equations of state (EOS), the Steger-Warming method becomes inapplicable and the Lax–Friedrichs method should be used for the numerical flux splitting. Following the formulation, the updated scheme is validated by a series of comparisons with theoretical and experimental data. The validation shows that the modified DCD scheme performs very well for supercavitating flows in the presence of steep gradients of both density and EOS. Several one-fluid cavitation models and speed of sound (SoS) models are compared for the numerical investigation of supercavitating flows.