Zooming into Vlasov-Poisson using the characteristic mapping method
ORAL
Abstract
We propose an efficient semi-Lagrangian characteristic mapping method for solving the one+one-dimensional Vlasov-Poisson equations with high precision on a coarse grid. The flow map is evolved numerically with a gradient-augmented level-set method and exponential resolution in linear time is obtained. Global third order convergence in space and time is shown and conservation properties are assessed. For benchmarking we consider Landau damping and the two-stream instability. We compare the results with a classical pseudo-spectral method. The extreme fine-scale resolution features are illustrated with zooms showing the method's capabilities of going beyond the limit of currently available schemes.
*The authors were granted access to the HPC resources of IDRIS under the allocation No. AD012A01664R1 attributed by Grand Equipement National de Calcul Intensif (GENCI).Centre de Calcul Intensif d'Aix-Marseille is acknowledged for granting access to its high performance computing resources.The authors acknowledge partial funding from the Agence Nationale de la Recherche (ANR), project CM2E, grant ANR-20-CE46-0010-01.
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Publication:P. Krah, X.-Y. Yin, J. Bergmann, J.-C. Nave and K. Schneider. A Characteristic Mapping Method for Vlasov–Poisson with extreme resolution properties Preprint, 08/2023
X.-Y. Yin, O. Mercier, B. Yadav, K. Schneider and J.-C. Nave. A Characteristic Mapping Method for the two-dimensional incompressible Euler equations. J. Comput. Phys., 424, 109781, 2021.
Presenters
Kai Schneider
Institut de Mathematiques Marseille, Aix-Marseille University
Aix-Marseille University
Authors
Philipp Krah
I2M, Aix-Marseille Université, France
Julius Bergmann
I2M, Aix Marseille Université, France and TU Berlin, Germany
Xi-Yuan Yin
LMFA, Ecole Centrale de Lyon, Université de Lyon, France
Jean-Christophe Nave
McGill University, Montreal, Canada
Kai Schneider
Institut de Mathematiques Marseille, Aix-Marseille University
