On the practical use of high-order methods for hyperbolic systems

The paper tests a number of high order methods on a variety of dynamic problems in one, two, and three space dimensions. The problems covered include wave propagation phenomena as well as an asymptotic approach to a steady state. Consideration is given to both smooth and shocked flows. It is shown that the methods compared require only minor modifications of many existing second-order schemes. Further, the results show that significant gains can be expected from the use of fourth-order methods. Finally, spectral methods are also considered for some of the problems presented.