Boundary optimized diagonal-norm SBP operators

Ken Mattsson* (Corresponding Author), Martin Almquist, Edwin van der Weide

*Corresponding author for this work

    Research output: Contribution to journalArticleAcademicpeer-review

    4 Citations (Scopus)
    1 Downloads (Pure)

    Abstract

    By using non-equispaced grid points near boundaries, we derive boundary optimized first derivative finite difference operators, of orders up to twelve. The boundary closures are based on a diagonal-norm summation-by-parts (SBP) framework, thereby guaranteeing linear stability on piecewise curvilinear multi-block grids. The new operators lead to significantly more efficient numerical approximations, compared with traditional SBP operators on equidistant grids. We also show that the non-uniform grids make it possible to derive operators with fewer one-sided boundary stencils than their traditional counterparts. Numerical experiments with the 2D compressible Euler equations on a curvilinear multi-block grid demonstrate the accuracy and stability properties of the new operators.

    Original languageEnglish
    Pages (from-to)1261-1266
    Number of pages6
    JournalJournal of computational physics
    Volume374
    DOIs
    Publication statusPublished - 1 Dec 2018

    Keywords

    • Euler equations
    • Finite difference methods
    • High order accuracy
    • Stability
    • Boundary treatment

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