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

We combine existing discretization methods to obtain a simplified numerical formulation of partial derivative equations posed on multi-block/element domains. The interfaces (conforming or non-conforming) between blocks are treated with inner-product-preserving interpolation operators. The result is a single set of high-order multi-block summation-by-parts operators that encapsulates both the metric terms and the interface treatments. This enables for a clean 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 both for linear and nonlinear equations, since no problem-specific interface conditions must be derived and implemented. The theoretical developments are valid for all discretization methods that are included in the summation-by-parts framework. 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 multiblock domain