The singular limits of solutions to the Riemann problem for the liquid–gas two-phase isentropic flow model

Abstract

All the possible Riemann solutions are constructed in fully explicit forms for the one-dimensional inviscid liquid–gas two-phase isentropic flow model of drift-flux type. The concentration and cavitation phenomena are observed and investigated in the Riemann solutions when the pressure in the mixture momentum equation tends to zero. It is proved rigorously that the Riemann solution consisting of a 1-shock wave, 2-contact discontinuity, and 3-shock wave converges to a delta shock wave solution. By comparison, the Riemann solution consisting of a 1-rarefaction wave, 2-contact discontinuity, and 3-rarefaction wave converges to a solution consisting of 1-contact discontinuity, the vacuum state, and 3-contact discontinuity.