Repositorio UFRO · Omeka S

Extension of the ENO-ET Reconstruction Scheme to Two Space Dimensions on Cartesian Meshes in Conjunction with the ADER Approach

Primer Autor	Montecinos, Gino I.
Co-autores	Toro, Eleuterio F.
Título	Extension of the ENO-ET Reconstruction Scheme to Two Space Dimensions on Cartesian Meshes in Conjunction with the ADER Approach
Editorial	GLOBAL SCIENCE PRESS
Revista	EAST ASIAN JOURNAL ON APPLIED MATHEMATICS
Lenguaje	en
Resumen	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 numer-ical schemes for approximating hyperbolic equations numerically. This theoretical re-sult 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 prob-lems 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 lin-ear 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.
Fecha Publicación	2023
Tipo de Recurso	artículo original
doi	10.4208/eajam.2022-352.280423
Formato Recurso	PDF
Palabras Claves	ENO reconstruction WENO reconstruction ADER schemes
Ubicación del archivo	http://dx.doi.org/10.4208/eajam.2022-352.280423
Categoría OCDE	Matemáticas
Materias	reconstrucción ENO reconstrucción WENO Esquemas ADER
Versión del recurso (Recomendado-único)	versión publicada
Tipo de ruta	suscripción
Access Rights	metadata
Derechos de acceso	metadata
Id de Web of Science	WOS:001016455600013
Página de inicio (Recomendado-único)	759.0
Página final (Recomendado-único)	790
Identificador del recurso (Mandatado-único)	artículo original
ISSN	2079-7362
Categoría WOS	Matemáticas