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

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    Abstract

    Optimal explicit Runge-Kutta (ERK) schemes with large stable step sizes are developed for method-of-lines discretizations based on the spectral difference (SD) spatial discretization on quadrilateral grids. These methods involve many stages and provide the optimal linearly stable time step for a prescribed SD spectrum and the minimum leading truncation error coefficient, while admitting a low-storage implementation. Using a large number of stages, the new ERK schemes lead to efficiency improvements larger than 60% over standard ERK schemes for 4th- and 5th-order spatial discretization.
    Original languageEnglish (US)
    Title of host publicationProceedings of the 11th Finnish Mechanics Days
    PublisherUniversity of Oulu
    StatePublished - 2012

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