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Volume 35, Issue 4
A Characteristic Mapping Method for Vlasov-Poisson with Extreme Resolution Properties

Philipp Krah, Xi-Yuan Yin, Julius Bergmann, Jean-Christophe Nave & Kai Schneider

DOI: 10.4208/cicp.OA-2024-0012

Commun. Comput. Phys., 35 (2024), pp. 905-937.

Published online: 2024-05

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  • 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 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 linear and nonlinear Landau damping and the two-stream instability. We compare the results with a Fourier pseudo-spectral method and results from the literature. The extreme fine-scale resolution features are illustrated showing the method’s capabilities to efficiently treat filamentation in fusion plasma simulations.

  • Keywords

Characteristic mapping method, kinetic equations, Vlasov-Poisson, plasma.

  • AMS Subject Headings

35Q83, 65M25, 68W10, 76X05

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{CiCP-35-905, author = {Krah , PhilippYin , Xi-YuanBergmann , JuliusNave , Jean-Christophe and Schneider , Kai}, title = {A Characteristic Mapping Method for Vlasov-Poisson with Extreme Resolution Properties}, journal = {Communications in Computational Physics}, year = {2024}, volume = {35}, number = {4}, pages = {905--937}, 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 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 linear and nonlinear Landau damping and the two-stream instability. We compare the results with a Fourier pseudo-spectral method and results from the literature. The extreme fine-scale resolution features are illustrated showing the method’s capabilities to efficiently treat filamentation in fusion plasma simulations.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2024-0012}, url = {http://global-sci.org/intro/article_detail/cicp/23089.html} }
TY - JOUR T1 - A Characteristic Mapping Method for Vlasov-Poisson with Extreme Resolution Properties AU - Krah , Philipp AU - Yin , Xi-Yuan AU - Bergmann , Julius AU - Nave , Jean-Christophe AU - Schneider , Kai JO - Communications in Computational Physics VL - 4 SP - 905 EP - 937 PY - 2024 DA - 2024/05 SN - 35 DO - http://doi.org/10.4208/cicp.OA-2024-0012 UR - https://global-sci.org/intro/article_detail/cicp/23089.html KW - Characteristic mapping method, kinetic equations, Vlasov-Poisson, plasma. AB -

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 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 linear and nonlinear Landau damping and the two-stream instability. We compare the results with a Fourier pseudo-spectral method and results from the literature. The extreme fine-scale resolution features are illustrated showing the method’s capabilities to efficiently treat filamentation in fusion plasma simulations.

Krah , PhilippYin , Xi-YuanBergmann , JuliusNave , Jean-Christophe and Schneider , Kai. (2024). A Characteristic Mapping Method for Vlasov-Poisson with Extreme Resolution Properties. Communications in Computational Physics. 35 (4). 905-937. doi:10.4208/cicp.OA-2024-0012
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