Minimum storage Runge-Kutta schemes for computational acoustics

In this paper, an implementation of some Runge-Kutta schemes that requires 2N-storage, where N is the number of degrees of freedom of the system is proposed. It is shown that, some Runge-Kutta schemes for wave propagation proposed by Hu, Hussaini and Manthey [1] can be written by using our implementation. Thus, we provide an alternative to the 2N-storage implementation proposed by Stanescu and Habashi [2] which follows the approach of Williamson [3], Carpenter and Kennedy [4] and others. In addition, new Runge-Kutta schemes with small dissipation and dispersion errors that can be written also by using our implementation are given. Finally, the results of some numerical experiments are presented to compare the behaviour of these methods.