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Numerical Entropy and Adaptivity for Finite Volume Schemes

Published online by Cambridge University Press:  20 August 2015

Gabriella Puppo  and
Matteo Semplice
Gabriella Puppo*
Affiliation:
Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italia
Matteo Semplice*
Affiliation:
Dipartimento di Fisica e Matematica, Università dell’Insubria, Via Valleggio 11, 22100 Como, Italia
*
Corresponding author.Email:gabriella.puppo@polito.it
Email:matteo.semplice@uninsubria.it
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Abstract

We propose an a-posteriori error/smoothness indicator for standard semi-discrete finite volume schemes for systems of conservation laws, based on the numerical production of entropy. This idea extends previous work by the first author limited to central finite volume schemes on staggered grids. We prove that the indicator converges to zero with the same rate of the error of the underlying numerical scheme on smooth flows under grid refinement. We construct and test an adaptive scheme for systems of equations in which the mesh is driven by the entropy indicator. The adaptive scheme uses a single nonuniform grid with a variable timestep. We show how to implement a second order scheme on such a space-time non uniform grid, preserving accuracy and conservation properties. We also give an example of a p-adaptive strategy.

Keywords

65M0865M5076M12Finite volume schemeshyperbolic systemslocal grid refinemententropy
Type
Research Article
Information
Communications in Computational Physics , Volume 10 , Issue 5 , November 2011 , pp. 1132 - 1160
Copyright
Copyright © Global Science Press Limited 2011

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