An Energy Stable Summation-by-parts Formulation for General Multi-block and Hybrid Meshes

• Most high order methods for solving conservation laws can be shown to satisfy a summation-by-parts rule. In this work we present a general framework for multi-block and multi-element summation-by-parts implementations in several dimensions that includes most, if not all of the previously known schemes on summation-by-parts form. This includes finite volume, spectral and nodal discontinuous Galerkin methods, as well as high order multi-block finite difference schemes on curvilinear domains. We use the framework to derive general conditions for conservation and stability, and formulate extended representations of conservative and energy stable couplings between completely general multi-block, multi-element or hybrid meshes.

Ämnesord

NATURVETENSKAP  -- Matematik -- Beräkningsmatematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Computational Mathematics (hsv//eng)

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