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

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Authors
Kozdon, Jeremy E.
Wilcox, Lucas C.
Subjects
summation-by-parts
weak enforcement
high-order nite di erence methods
coupling
stability
accuracy
projection operator
variational form
interface
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2015-05-22
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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.
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Article
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Applied Mathematics
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This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.
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