Communications on Applied Mathematics and Computation >

2023 , Vol. 5 >Issue 2: 776 - 852

DOI: https://doi.org/10.1007/s42967-021-00147-0

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

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  • 1 Laboratory of Applied Mathematics, DICAM, University of Trento, Trento, Italy;
    2 Department of Mathematics, University of Trento, Trento, Italy;
    3 Department of Natural Sciences and Technology, Universidad de Aysén, Obispo Vielmo 62, Coyhaique, Chile

Received date: 2020-11-30

  Revised date: 2021-05-31

  Online published: 2023-05-26

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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 L1-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.

Key words： Hyperbolic equations; High-order ADER; ENO/m-ENO/WENO; Novel reconstruction technique AENO/m-AENO

Cite this article

Eleuterio F. Toro, Andrea Santacá, Gino I. Montecinos, Morena Celant, Lucas O. Müller . AENO: a Novel Reconstruction Method in Conjunction with ADER Schemes for Hyperbolic Equations[J]. Communications on Applied Mathematics and Computation, 2023 , 5(2) : 776 -852 . DOI: 10.1007/s42967-021-00147-0

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