Interaction of weak shocks in drift-flux model of compressible two-phase flows

We consider the Riemann problem for an isothermal no-slip compressible gas-liquid drift-flux model of multi-phase flows governing two mass conservation equations and one mixture momentum equation. We establish a global result for the existence and uniqueness of a solution to the Riemann problem. We obtain one parameter family of elementary wave curves explicitly. Further, we derive a necessary and sufficient condition to ensure the existence of a shock wave or a simple wave for a 1-family and a 3-family of characteristics on the initial data in the solution of the Riemann problem. Finally, we prove the result of Von Neumann's concerning the overtaking of two weak shocks of same family.