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 high-order multi-block operator form that encapsulates both metric terms as well interface treatments. This enables compact description of scheme mimics essential features its continuous counterpart. Furthermore, stability analysis domain linear nonlinear equations, since no problem-specific conditions need be derived implemented. exemplify combined technique by considering nonlinearly stable discrete formulation incompressible Navier-Stokes perform calculations an underlying domain.