CWENO: Uniformly accurate reconstructions for balance laws
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- by I. Cravero, G. Puppo, M. Semplice and G. Visconti PDF
- Math. Comp. 87 (2018), 1689-1719 Request permission
Abstract:
In this paper we introduce a general framework for defining and studying essentially nonoscillatory reconstruction procedures of arbitrarily high order of accuracy, interpolating data in the central stencil around a given computational cell ($\mathsf {CWENO}$). This technique relies on the same selection mechanism of smooth stencils adopted in $\mathsf {WENO}$, but here the pool of candidates for the selection includes polynomials of different degrees. This seemingly minor difference allows us to compute the analytic expression of a polynomial interpolant, approximating the unknown function uniformly within a cell, instead of only at one point at a time. For this reason this technique is particularly suited for balance laws for finite volume schemes, when averages of source terms require high order quadrature rules based on several points; in the computation of local averages, during refinement in $h$-adaptive schemes; or in the transfer of the solution between grids in moving mesh techniques, and in general when a globally defined reconstruction is needed. Previously, these needs have been satisfied mostly by ENO reconstruction techniques, which, however, require a much wider stencil than the $\mathsf {CWENO}$ reconstruction studied here, for the same accuracy.References
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Additional Information
- I. Cravero
- Affiliation: Dipartimento di Matematica, Università di Torino, Via C. Alberto, 10, Torino, Italy
- MR Author ID: 324467
- Email: isabella.cravero@unito.it
- G. Puppo
- Affiliation: Dipartimento di Scienza e Alta Tecnologia, Università dell’Insubria, Via Valleggio, 11, Como, Italy.
- MR Author ID: 355386
- Email: gabriella.puppo@uninsubria.it
- M. Semplice
- Affiliation: Dipartimento di Matematica, Università di Torino, Via C. Alberto, 10, Torino, Italy
- MR Author ID: 638685
- Email: matteo.semplice@unito.it
- G. Visconti
- Affiliation: Dipartimento di Scienza e Alta Tecnologia, Università dell’Insubria, Via Valleggio, 11, Como, Italy
- Address at time of publication: IGPM–RWTH Aachen University, Templergraben 55, D-52056 Aachen, Germany
- MR Author ID: 1152946
- Email: visconti@igpm.rwth-aachen.de
- Received by editor(s): July 26, 2016
- Received by editor(s) in revised form: March 11, 2017
- Published electronically: November 2, 2017
- Additional Notes: The third author is the corresponding author.
This work was supported by INDAM GNCS-2016 grant “Metodi numerici per la quantificazione dellâincertezza in equazioni iperboliche e cinetiche” - © Copyright 2017 American Mathematical Society
- Journal: Math. Comp. 87 (2018), 1689-1719
- MSC (2010): Primary 65M08; Secondary 65M12
- DOI: https://doi.org/10.1090/mcom/3273
- MathSciNet review: 3787389