Stable coupling of nonconforming, high-order finite difference methods
Kozdon, Jeremy E.
Wilcox, Lucas C.
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A methodology for handling block-to-block coupling of nonconforming, 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 functions; we specifically consider discontinuous, piecewise polynomial functions. The constructed projection operators are compatible 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, nonconforming block-to-block interfaces. To further demonstrate the power of the coupling procedure, we show how it allows for the development of a provably energy stable coupling between curvilinear finite difference methods and a curved-triangle discontinuous Galerkin method. The theoretical results are verified through numerical solutions on curved meshes as well as eigenvalue analysis.
Approved for public release; distribution is unlimitedThe article of record as published may be found at http://dx.doi.org/10.1137/15M1022823
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