Concentration and cavitation for the modified Chaplygin two-phase flow model at the vanishing pressure limit

Abstract

Creation of delta shock and vacuum in Riemann solutions under the pressureless circumstance is derived from the corresponding ones from the modified Chaplygin flow model in the content of liquid-gas two-phase flow by sending the two perturbed parameters go to zero in the pressure simultaneously. The associated concentration and cavitation effects can be carefully observed and analyzed at such limiting procedure. It should be stressed that there exist three possible occurring scenarios about the vacuum formation by taking into account the virtual velocity within vacuum region due to the different convergence rates of the two perturbed parameters.