Quadratic conservative scheme for relativistic Vlasov–Maxwell system

Takashi Shiroto, Naofumi Ohnishi, Yasuhiko Sentoku

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


For more than half a century, most of the plasma scientists have encountered a violation of the conservation laws of charge, momentum, and energy whenever they have numerically solved the first-principle equations of kinetic plasmas, such as the relativistic Vlasov–Maxwell system. This fatal problem is brought by the fact that both the Vlasov and Maxwell equations are indirectly associated with the conservation laws by means of some mathematical manipulations. Here we propose a quadratic conservative scheme, which can strictly maintain the conservation laws by discretizing the relativistic Vlasov–Maxwell system. A discrete product rule and summation-by-parts are the key players in the construction of the quadratic conservative scheme. Numerical experiments of the relativistic two-stream instability and relativistic Weibel instability prove the validity of our computational theory, and the proposed strategy will open the doors to the first-principle studies of mesoscopic and macroscopic plasma physics.

Original languageEnglish
Pages (from-to)32-50
Number of pages19
JournalJournal of Computational Physics
Publication statusPublished - 2019 Feb 15


  • Computational plasma physics
  • Quadratic conservative scheme
  • Relativistic Vlasov–Maxwell system
  • Structure-preserving algorithm

ASJC Scopus subject areas

  • Numerical Analysis
  • Modelling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


Dive into the research topics of 'Quadratic conservative scheme for relativistic Vlasov–Maxwell system'. Together they form a unique fingerprint.

Cite this