Singular limit solutions and wave interactions in a bi-fluid flow model

This study examines one-dimensional isentropic inviscid bi-fluid (liquid-gas) flow, known as drift-flux flow, and explicitly derives all possible elementary wave solutions for the two-piece Riemann problem. Additionally, we examine the formation of δ-shock waves and vacuum states using the vanishing pressure method. The convergence of solutions from the pressure-regularized system to the pressureless system in the vanishing pressure limit is rigorously established. Furthermore, a comprehensive analysis of all potential wave interactions, both within the same family and across different families of elementary waves, is conducted through phase plane analysis. We further analyze the interactions of delta shock waves arising in the pressureless case.