Optimized explicit Runge-Kutta schemes for the spectral difference method applied to wave propagation problems

Abstract

Explicit Runge-Kutta schemes with large stable step sizes are developed for integration of high-order spectral difference spatial discretizations on quadrilateral grids. The new schemes permit an effective time step that is substantially larger than the maximum admissible time step of standard explicit Runge-Kutta schemes available in the literature. Furthermore, they have a small principal error norm and admit a low-storage implementation. The advantages of the new schemes are demonstrated through application to the Euler equations and the linearized Euler equations. © 2013 Society for Industrial and Applied Mathematics.