A class of exact solutions for the euler equations with sources: Part I

A number of engineering problems, such as those encountered in combustion and multiphase flows for example, use systems of partial differential equations to which must be added algebraic expressions (or source terms) that model certain interactions between particular parts of the system. It is often the case that such sources have a primary responsibility for generation of the motion of the fluid. be very valuable to have some relevant problems, that can be solved exactly, to use as tests for the numerical methods that are generally required to solve the real-world problems. The present paper extends the work by Clarke [1] and Clarke and Toro [2] which described an exact analytical solution of the Euler equations for a particular choice of source terms.