Stable Coupling of Nonconforming, High-Order Finite Difference Methods
| Autor: | Kozdon, Jeremy E., Wilcox, Lucas C. |
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| Rok vydání: | 2014 |
| Předmět: | |
| Zdroj: | SIAM Journal on Scientific Computing, 38(2), pp.A923-A952 (2016) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1137/15M1022823 |
| Popis: | 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 simulations on curved meshes as well as eigenvalue analysis. Comment: 30 pages, 7 figures, 4 tables |
| Databáze: | arXiv |
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