The Riemann problem for a spray model

A spray model is presented as a simplified two-phase flow model. The fluid flow of interest is the first phase, and the second phase of incoming fluid spray plays the role for a source. This source contributes two nonconservative terms to the system for the balance of momentum and balance of energy. The model is described by four governing equations for the dynamics of the main stream together with the convection equation for the spray of incoming fluid. The system is not strictly hyperbolic and resonance phenomenon appears. In particular, assuming that the incoming fluid spray is constant, we can solve the Riemann problem. It turns our that there may by up to three distinct solutions. Further, solutions may contain multiple waves of the same speed associated with different characteristic fields.