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Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain


Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email:

On the Verification of Adaptive Three-dimensional Multiresolution Computations of the Magnetohydrodynamic Equations

Journal of Applied Nonlinear Dynamics 7(3) (2018) 231--242 | DOI:10.5890/JAND.2018.09.002

Anna Karina Fontes Gomes$^{1}$, Margarete Oliveira Domingues$^{2}$, Odim Mendes$^{3}$, Kai Schneider$^{4}$

$^{1}$ Post-graduation program in Applied Computing, Brazilian Institute of Space Sciences, São José dos Campos, 12227-010, Brazil

$^{2}$ Associated Laboratory for Computing and AppliedMathematics, Brazilian Institute of Space Sciences, São José dos Campos, 12227-010, Brazil

$^{3}$ Space Geophysics Division, Brazilian Institute of Space Sciences, São José dos Campos, 12227-010, Brazil

$^{4}$ Institut de Mathématiques de Marseille, Aix-Marseille Université CNRS, Centrale Marseille, I2M UMR 7373, 13453, Marseille, France

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Magnetohydrodynamics is an important tool to study the dynamics of Space Physics. In this context, we introduce a three-dimensional magnetohydrodynamic solver with divergence-cleaning in the adaptive multiresolution CARMEN code. The numerical scheme is based on a finite volume discretization that ensures the conservation of physical quantities. The adaptive multiresolution approach allows for automatic identification of local structures in the numerical solution and thus provides an adaptive mesh refined only in regions where the solution needs more improved resolution. We assess the threedimensional magnetohydrodynamic CARMEN code and compare its results with the ones from the well-known FLASH code.


The authors thank the Brazilian agencies CNPq (306038/2015 − 3,312246/2013 − 7), FINEP/CTINFRA (01120527−00), and FAPESP (2015/50403−0,2015/25624−2) projects for financial support. We thank Dr. Olivier Roussel for developing the original Carmen Code and for the fruitful scientific discussions. We also thank Eng. V. E. Menconi for his helpful computational assistance. The Flash software used in this work was in part developed by the DOE NNSA-ASC OASCR Flash Center at the University of Chicago. AKFG thanks CNPq for the PhD scholarship (project 141741/2013−9). MD thankfully acknowledges financial support from Ecole Centrale Marseille. KS acknowledges financial support from the ANR-DFG, grant AIFIT, and support by the French Research Federation for Fusion Studies within the framework of the European Fusion Development Agreement (EFDA).


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