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

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 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.