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A High-Order Compact Limiter Based on Spatially Weighted Projections for the Spectral Volume and the Spectral Differences Method

Lamouroux, Raphaël and Gressier, Jérémie and Grondin, Gilles A High-Order Compact Limiter Based on Spatially Weighted Projections for the Spectral Volume and the Spectral Differences Method. (2016) Journal of Scientific Computing, 67 (1). 375-403. ISSN 0885-7474

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Official URL: http://dx.doi.org/10.1007/s10915-015-0084-6

Abstract

This paper exposes the theoretical developments needed to design a class of spatially weighted polynomial projections used in the definition of a compact limiter dedicated to high-order methods. The spectral volume framework and its integral representation of the solution is used to introduce the degree reduction of the polynomial interpolation. The degree reduction is conducted through a linear projection onto a smaller polynomial space. A particular care is taken regarding the conservativity property and results in a parametric framework where projections can be monitored with spatial weights. These projections are used to define a simple and compact high-order limiting procedure, the SWeP limiter. Then, numerical evaluations are performed using the spectral differences method for the mono-dimensional Euler equations and demonstrate the high-order behavior of the SWeP limiter.

Item Type:Article
Additional Information:Thanks to Springer editor. The definitive version is available at http://link.springer.com/ The original PDF of the article can be found at Journal of Scientific Computing website : http://link.springer.com/article/10.1007%2Fs10915-015-0084-6
Audience (journal):International peer-reviewed journal
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Institution:Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE)
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Deposited By: Raphael Lamouroux
Deposited On:07 Dec 2015 10:00

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