Abstract

Having studied shocks and rarefaction fans for non-linear scalar conservation laws in the previous chapter, we now move on to a study of the same for systems of hyperbolic conservation laws. We use the Euler equations as an example. Discontinuous solutions of the Euler equations - shocks and contact discontinuities - are studied in detail. We then study isentropic flow and rarefaction fans in detail. The Riemann problem is shown to be an essential building block for the numerical solution of systems of hyperbolic conservation laws. The solution of the hydrodynamical Riemann problem is presented in detail. It is applied to several shock tube problems and the results are discussed.

Sections of the Chapter