A NONCONSERVATIVE HYPERBOLIC SYSTEM MODELING SPRAY DYNAMICS. PART I: SOLUTION OF THE RIEMANN PROBLEM

Abstract

The flow of a spray of liquid droplets in a gas is modeled by a convection-diffusion system whose convection part is hyperbolic and written in nonconservation form. As a first step towards the numerical solution of the second order system, we solve Riemann problem for the convection part: the shock waves solutions of the latter system are defined as the limit of traveling waves solution of the whole system when the diffusion is neglected. The structure of the first order system allows to define discontinuous solutions associated with the linearly degenerate fields. The definition of rarefaction waves solution of the latter system is standard and we solve Riemann problems at least for initial data with small variation.