A model system with two equations $\hfill $ 14

$ \qquad 2.4 \quad $ Unidimensional linear acoustics $\hfill $ 17

$ \qquad 2.5 \quad $ Characteristic variables $\hfill $ 21

$ \qquad 2.6 \quad $ A family of model systems with three equations $\hfill $ 25

$ \qquad 2.7 \quad $ First order upwind-centered finite volumes $\hfill $ 27

[**3) $ \,\, $ Gas dynamics with the Roe method** ]{}

$ \qquad 3.1 \quad $ Nonlinear acoustics in one space dimension $\hfill $ 29

$ \qquad 3.2 \quad $ Linearization of the gas dynamics equations $\hfill $ 30

$ \qquad 3.3 \quad $ Roe matrix $\hfill $ 33

$ \qquad 3.4 \quad $ Roe flux $\hfill $ 35

$ \qquad 3.5 \quad $ Entropy correction $\hfill $ 38

$ \qquad 3.6 \quad $ Nonlinear flux boundary conditions $\hfill $ 40

[**4) $ \,\, $ Second order and two space dimensions** ]{}

$ \qquad 4.1 \quad $ Towards second order accuracy $\hfill $ 42

$ \qquad 4.2 \quad $ The method of lines $\hfill $ 43

$ \qquad 4.3 \quad $ The method of Van Leer $\hfill $ 45

$ \qquad 4.4 \quad $ Second order accurate finite volume method for 