AENO: a Novel Reconstruction Method in Conjunction with ADER Schemes for Hyperbolic Equations

In this paper, we present a novel spatial reconstruction scheme, called AENO , that results from a special averaging of the ENO polynomial and its closest neighbour, while retaining the stencil direction decided by the ENO choice. A variant of the scheme, called m-AENO, results from averaging the mo...

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Bibliographic Details
Published in:Communications on Applied Mathematics and Computation (Online) 2023-06, Vol.5 (2), p.776-852
Main Authors: Toro, Eleuterio F., Santacá, Andrea, Montecinos, Gino I., Celant, Morena, Müller, Lucas O.
Format: Article
Language:English
Subjects:
Applications of Mathematics
Computational Science and Engineering
Mathematics
Mathematics and Statistics
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Summary:In this paper, we present a novel spatial reconstruction scheme, called AENO , that results from a special averaging of the ENO polynomial and its closest neighbour, while retaining the stencil direction decided by the ENO choice. A variant of the scheme, called m-AENO, results from averaging the modified ENO (m-ENO) polynomial and its closest neighbour. The concept is thoroughly assessed for the one-dimensional linear advection equation and for a one-dimensional non-linear hyperbolic system, in conjunction with the fully discrete, high-order ADER approach implemented up to fifth order of accuracy in both space and time. The results, as compared to the conventional ENO, m-ENO and WENO schemes, are very encouraging. Surprisingly, our results show that the L 1 -errors of the novel AENO approach are the smallest for most cases considered. Crucially, for a chosen error size, AENO turns out to be the most efficient method of all five methods tested.
ISSN:2096-6385
2661-8893
DOI:10.1007/s42967-021-00147-0