The Euler equations in one space dimension

Since almost all computing methods for the Euler equations in two and three space dimensions rely heavily on techniques developed for the one-dimensional case, we devote a full chapter to the one-dimensional Euler equations. In the one-dimensional case many intersting analytic aspects can be brought to light, and this we do first. The shock tube problem is a very useful test problem for discretization schemes; we will present its analytic solution. Then we turn to discretization methods. More extentive introductions to numerical methods for the Euler equationsare given by Godlewski and Raviart (1996), Kroner (1997), Laney (1998), Majda (1984), Toro (1997), Smoller (1983), Hirsch (1990).