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Adaptive two- and three-dimensional multiresolution computations of resistive magnetohydrodynamics

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Abstract

Fully adaptive computations of the resistive magnetohydrodynamic (MHD) equations are presented in two and three space dimensions using a finite volume discretization on locally refined dyadic grids. Divergence cleaning is used to control the incompressibility constraint of the magnetic field. For automatic grid adaptation a cell-averaged multiresolution analysis is applied which guarantees the precision of the adaptive computations, while reducing CPU time and memory requirements. Implementation issues of the open source code CARMEN-MHD are discussed. To illustrate its precision and efficiency different benchmark computations including shock-cloud interaction and magnetic reconnection are presented.

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Acknowledgments

We are indebted to Eng. V. E. Menconi for his invaluable computational assistance.

Funding

This work received financial support from the FAPESP (Grant: 2015/ 25624-2), CNPq (Grants: 302226/2018-4, 307083/2017-9, 306038/2015-3, 302226/2018-4), and FINEP (Grant: 0112052700) for financial support of this research. K.S. received partial support from the French Federation for Magnetic Fusion Studies (FR-FCM) and the Eurofusion consortium, funded by the Euratom research and training programme 2014–2018 and 2019–2020 under grant agreement no. 633053.

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Authors and Affiliations

  1. Federal Institute of São Paulo, Cubatão, São Paulo, Brazil

    Anna Karina Fontes Gomes

  2. National Institute for Space Research, São José dos Campos, São Paulo, Brazil

    Margarete Oliveira Domingues & Odim Mendes

  3. Aix-Marseille Université, CNRS, Centrale Marseille, I2M, Marseille, France

    Kai Schneider

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  1. Anna Karina Fontes Gomes
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  2. Margarete Oliveira Domingues
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Correspondence to Anna Karina Fontes Gomes.

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Communicated by: Silas Alben

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Gomes, A.K.F., Domingues, M.O., Mendes, O. et al. Adaptive two- and three-dimensional multiresolution computations of resistive magnetohydrodynamics. Adv Comput Math 47, 22 (2021). https://doi.org/10.1007/s10444-021-09845-y

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