ASHEE Multiphase fluid dynamic model conceived for compressible mixtures composed of gaseous components and solid particle phases. All phases are treated using the Eulerian approach, identifying a solid phase as a class of particles with similar dynamical properties. The physical model is based on the equilibrium-Eulerian approach while the gas-particle momentum non-equilibrium is approximated by a prognostic equation accurate to the first order. As a result, the model reduces to a single (vector) momentum equation and one energy equation for the mixture (corrected to account for non-equilibrium terms and mixture density fluctuations) and one continuity equation for each gaseous or solid component. In addition, Lagrangian particles are injected in the domain and “two/four-way” coupled with the Eulerian field. Discretization is based on the Finite-Volume method on an unstructured grid. The numerical solution adopts a segregated semi-implicit approach.