Optimized low-order explicit Runge-Kutta schemes for high- order spectral difference method

摘要

Optimal explicit Runge-Kutta (ERK) schemes with large stable step sizes aredeveloped for method-of-lines discretizations based on the spectral difference (SD) spatial discretizationon quadrilateral grids. These methods involve many stages and provide the optimallinearly stable time step for a prescribed SD spectrum and the minimum leading truncation errorcoefficient, while admitting a low-storage implementation. Using a large number of stages, thenew ERK schemes lead to efficiency improvements larger than 60% over standard ERK schemesfor 4th- and 5th-order spatial discretization.