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Numerical Entropy and Adaptivity for Finite Volume Schemes

Numerical Entropy and Adaptivity for Finite Volume Schemes
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Year:    2011

Communications in Computational Physics, Vol. 10 (2011), Iss. 5 : pp. 1132–1160

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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.250909.210111a

Communications in Computational Physics, Vol. 10 (2011), Iss. 5 : pp. 1132–1160

Published online:    2011-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    29

Keywords:   

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