The transition of Riemann solutions for the drift-flux model with the pressure law for the extended Chaplygin gas

Abstract

The complete Riemann solutions for the drift-flux model with the pressure law given both for the extended Chaplygin gas and also for the Chaplygin gas are solved in fully explicit forms. By the Chaplygin gas, we mean that the fluid obeys the pressure-density relation where the pressure is negative and also the inverse of the density, and further the extended Chaplygin gas is the extension of the Chaplygin gas by adding up the barotropic equation of state with higher orders. Furthermore, the transition of Riemann solutions for this model is analyzed carefully when the pressure law changes from the extended Chaplygin gas to the Chaplygin gas as all the perturbed parameters go to zero. The formation of delta shock solution from the Riemann solution consisting of 1-shock wave, 2-contact discontinuity, and 3-shock wave is identified and investigated in this limiting circumstance. In addition, the formation of the combination of three contact discontinuities from four different combinations of Riemann solutions is also inspected and studied in this limiting situation.