Provably stable, general purpose projection operators for high-order finite difference methods

Abstract

A methodology for handling block-to-block coupling of non-conforming, multiblock summation-by-parts finite difference methods is proposed. The coupling is based on the construction of projection operators that move a finite difference grid solution along an interface to a space of piecewise defined function; we specifically consider piecewise polynomial functions. The constructed projection operators are consistent with the underlying summation-by-parts energy norm. Using the linear wave equation in two dimensions as a model problem, energy stability of the coupled numerical method is proven for the case of curved, non-conforming block-to-block interfaces. To further demonstrate the power of the coupling procedure, we show how it allows for the developments of a provably energy stable coupling between curvilinear nite di erence methods and a curved-triangle discontinuous Galerkin method. The theoretical results are veri ed through numerical simulations on curved meshes as well as eigenvalue analysis.