A class of analytical solutions to the Euler equations with source terms: Part II

Models of combustion for gaseous reactants and multiphase flow can often be described by systems of hyperbolic partial differential equations that include the presence of algebraic source terms. The present work follows directly from a previous paper [1] that describes analytical solutions for the Euler equations that include purely positive contributions of mass, momentum, and energy from the sources. In this paper, the influence of source terms that include losses of momentum and energy is explored. are some lessons to be learnt about the physics of multiphase flows from the present theory, but its primary value is via the provision of test problems for numerical methods in the presence of sources.