A multi-domain summation-by-parts formulation for complex geometries

• We combine existing summation-by-parts discretization methods to obtain a simplified numerical framework for partial differential equations posed on complex multi-block/element domains. The interfaces (conforming or non-conforming) between blocks are treated with inner-product-preserving interpolation operators, and the result is a high-order multi-block operator on summation-by-parts form that encapsulates both the metric terms as well as the interface treatments. This enables for a compact description of the numerical scheme that mimics the essential features of its continuous counterpart. Furthermore, the stability analysis on a multi-block domain is simplified for both for linear and nonlinear equations, since no problem-specific interface conditions need to be derived and implemented. We exemplify the combined operator technique by considering a nonlinearly stable discrete formulation of the incompressible Navier-Stokes equations and perform calculations on an underlying multi-block domain. 

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Nyckelord

Summation-by-parts; Multi-block operators; Partial derivative approximations; Nonlinear stability

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