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Journal of Scientific Computing

Erschienen in:

22.07.2019

Extension of Tensor-Product Generalized and Dense-Norm Summation-by-Parts Operators to Curvilinear Coordinates

verfasst von: David C. Del Rey Fernández, Pieter D. Boom, Mark H. Carpenter, David W. Zingg

Erschienen in: Journal of Scientific Computing | Ausgabe 3/2019

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Abstract

Methodologies are presented that enable the construction of provably linearly stable and conservative high-order discretizations of partial differential equations in curvilinear coordinates based on generalized summation-by-parts operators, including operators with dense-norm matrices. Specifically, three approaches are presented for the construction of stable and conservative schemes in curvilinear coordinates using summation-by-parts (SBP) operators that have a diagonal norm but may or may not include boundary nodes: (1) the mortar-element approach, (2) the global SBP-operator approach, and (3) the staggered-grid approach. Moreover, the staggered-grid approach is extended to enable the development of stable dense-norm operators in curvilinear coordinates. In addition, collocated upwind simultaneous approximation terms for the weak imposition of boundary conditions or inter-element coupling are extended to curvilinear coordinates with the new approaches. While the emphasis in the paper is on tensor-product SBP operators, the approaches that are covered are directly applicable to multidimensional SBP operators.

Vorheriger Artikel A Comparison of the Explicit and Implicit Hybridizable Discontinuous Galerkin Methods for Nonlinear Shallow Water Equations

Nächster Artikel Correction to: ALORA: Affine Low-Rank Approximations

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Titel: Extension of Tensor-Product Generalized and Dense-Norm Summation-by-Parts Operators to Curvilinear Coordinates
verfasst von: David C. Del Rey Fernández
Pieter D. Boom
Mark H. Carpenter
David W. Zingg
Publikationsdatum: 22.07.2019
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 3/2019
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-019-01011-3

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