High order diamond differencing schemes |
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Authors: | Alain H bert |
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Affiliation: | aInstitut de Génie Nucléaire, École Polytechnique de Montréal, P.O. Box 6079, Station “Centre-Ville”, Montréal, Que., Canada H3C 3A7 |
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Abstract: | We present a generalization if the diamond differencing scheme to high-order spatial orders in one- and two-dimensional Cartesian geometries. Unlike existing variable-order nodal schemes our approach reduces to the conventional low-order diamond differencing scheme in the linear case and feature super convergence characteristics at all orders. This approach is demonstrated on one- and two-dimensional benchmark problems and is compared to spherical harmonics reference solutions. |
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