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

TL;DR

This paper develops optimized explicit Runge-Kutta schemes that enable larger stable time steps and efficient implementation for spectral difference methods in wave propagation simulations.

Contribution

The paper introduces new Runge-Kutta schemes with larger stable steps, low error norms, and low-storage features for spectral difference discretizations.

Findings

Schemes achieve significantly larger stable time steps.

Effective for Euler and linearized Euler equations.

Demonstrated improved efficiency in wave propagation problems.

Abstract

Explicit Runge-Kutta schemes with large stable step sizes are developed for integration of high order spectral difference spatial discretization 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.