@Article{EAJAM-13-759,
author = {Montecinos , Gino I. and Toro , Eleuterio F.},
title = {Extension of the ENO-ET Reconstruction Scheme to Two Space Dimensions on Cartesian Meshes in Conjunction with the ADER Approach},
journal = {East Asian Journal on Applied Mathematics},
year = {2023},
volume = {13},
number = {3},
pages = {759--790},
abstract = {<p style="text-align: justify;">Godunov’s Theorem [S.K. Godunov, Mat. Sb. 47 (1959)], stated more than
six decades ago, set the framework for understanding the limitations of linear numerical schemes for approximating hyperbolic equations numerically. This theoretical result sets one of the basic requirements for constructing high-order numerical schemes,
namely non-linearity. In the present article we are concerned with modifications to
essentially-non-oscillatory (ENO) non-linear reconstruction approach, along with fully
discrete ADER schemes to derive methods of arbitrary order of accuracy in space and
time. Here we extend a recently proposed ENO-ET scheme for one-dimensional problems to two space dimensions with Cartesian meshes. The methods are implemented
up to fifth order of accuracy and assessed via three scalar 2D problems, namely the linear advection equation, Burgers equation and a kinematic frontogenesis model used in
meteorology. Empirical convergence rates are studied for the classical ENO, classical
WENO and the newly proposed ENO-ET. For smooth solutions results from the newly
proposed ENO-ET reconstruction scheme are superior to those of conventional ENO in
terms of theoretically expected convergence rates and size of errors. Compared to the
results obtained with WENO reconstruction, the performance of ENO-ET for second and
third orders is superior. For discontinuous solutions, again ENO-ET is superior, in that it
captures wave amplitudes more accurately than ENO as accurate as WENO and, unlike
ENO, exhibits no spurious oscillations near discontinuities.</p>},
issn = {2079-7370},
doi = {https://doi.org/10.4208/eajam.2022-352.280423},
url = {http://global-sci.org/intro/article_detail/eajam/21729.html}
}