Power ENO methods: A fifth-order accurate weighted power ENO method.
type: Item
instance of: scholarly article
title: Power ENO methods: A fifth-order accurate weighted power ENO method.
zbMATH Open document ID: 1044.65071
author: Susana Serna
author: Antonio Marquina
published in: Journal of Computational Physics
publication date: 2004-03-14T00:00:00Z
review text: A new class of parabolic essentially non-oscillatory methods (\textit{power ENO methods}) is introduced for numerical approximation to nonlinear conservation laws. These methods are based on a class of limiters that contains \textit{minmod} and ENO limiters as a particular case, as well as the limiters based on the harmonic mean, used to design the PHM methods and harmonic ENO methods. The study is focused on ENO \textit{parabolas and the limiters on neighboring second-order differences} is applied in order to retain more information of fine scales. The main advantage of those methods with respect to the classical ENO methods is the improved behavior near discontinuities. In particular, a new fifth-order accurate weighted ENO method is proposed with a better behavior near jumps and corners than the WENO5 method of \textit{G. S. Jiang} and \textit{C. W. Shu} [J. Comput. Phys. 126, No. 1, 202--228 (1996; Zbl 0877.65065)]. A disadvantage of applying limiters on second-order differences is that there is a loss of accuracy near smooth inflection points. In numerical experiments where fine structures appear to be important (e. g., vortex regions), the weighted power ENO method shows substantial improvements in resolving fine scales, in spite of the improvements observed in standard numerical tests might seem to be minor. The paper is organized as follows: In Section 2 the new family of limiters is considered. Section 3 is focused on the new power ENO method: the advantages and disadvantages are discussed. The method is compared to the parabolic ENO method. In particular, the third-order accurate power ENO3 method is discussed. In Section 4, a new fifth-order accurate weighted power ENO method is described. This method is designed as a convex combination of the three parabolas used to define the third-order accurate Power ENO method, following a similar procedure to the one used by Jiang and Shu [loc. cit.]. In Section 5, the power ENO and weighted power ENO methods are te…
reviewed by: Leonid B. Chubarov
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 76M20
Mathematics Subject Classification ID: 76N15
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 35L65
zbMATH DE Number: 2056056
zbMATH Keywords: nonlinear conservation laws
zbMATH Keywords: discontinuities
zbMATH Keywords: ENO methods
zbMATH Keywords: WENO methods
zbMATH Keywords: limiters
zbMATH Keywords: finite difference method
zbMATH Keywords: total variation
zbMATH Keywords: numerical experiments
zbMATH Keywords: essentially non-oscillatory
MaRDI profile type: Publication
full work available at URL: j.jcp.2003.09.017
OpenAlex ID: W2128105245
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DOI: 10.1016/J.JCP.2003.09.017
description: scientific article; zbMATH DE number 2056056