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.

AENO: A Novel Reconstruction Method in Conjunction with ADER Schemes for Hyperbolic Equations / Toro, Ef; Santaca, A; Montecinos, Gi; Celant, M; Muller, Lo. - In: COMMUNICATIONS ON APPLIED MATHEMATICS AND COMPUTATION. - ISSN 2096-6385. - STAMPA. - 2023, 5:(2023), pp. 776-852. [10.1007/s42967-021-00147-0]

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

Toro, EF;Celant, M;Muller, LO
2023-01-01

Abstract

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.
2023
Toro, Ef; Santaca, A; Montecinos, Gi; Celant, M; Muller, Lo
AENO: A Novel Reconstruction Method in Conjunction with ADER Schemes for Hyperbolic Equations / Toro, Ef; Santaca, A; Montecinos, Gi; Celant, M; Muller, Lo. - In: COMMUNICATIONS ON APPLIED MATHEMATICS AND COMPUTATION. - ISSN 2096-6385. - STAMPA. - 2023, 5:(2023), pp. 776-852. [10.1007/s42967-021-00147-0]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/322053
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