Volume 10, Issue 5
Numerical Entropy and Adaptivity for Finite Volume Schemes

Gabriella Puppo & Matteo Semplice

Commun. Comput. Phys., 10 (2011), pp. 1132-1160.

Published online: 2011-10

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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.

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@Article{CiCP-10-1132, author = {}, title = {Numerical Entropy and Adaptivity for Finite Volume Schemes}, journal = {Communications in Computational Physics}, year = {2011}, volume = {10}, number = {5}, pages = {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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.250909.210111a}, url = {http://global-sci.org/intro/article_detail/cicp/7478.html} }
TY - JOUR T1 - Numerical Entropy and Adaptivity for Finite Volume Schemes JO - Communications in Computational Physics VL - 5 SP - 1132 EP - 1160 PY - 2011 DA - 2011/10 SN - 10 DO - http://doi.org/10.4208/cicp.250909.210111a UR - https://global-sci.org/intro/article_detail/cicp/7478.html KW - AB -

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.

Gabriella Puppo & Matteo Semplice. (2020). Numerical Entropy and Adaptivity for Finite Volume Schemes. Communications in Computational Physics. 10 (5). 1132-1160. doi:10.4208/cicp.250909.210111a
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