TY - JOUR

T1 - Quadratic conservative scheme for relativistic Vlasov–Maxwell system

AU - Shiroto, Takashi

AU - Ohnishi, Naofumi

AU - Sentoku, Yasuhiko

N1 - Funding Information:
T.S. wishes to appreciate the fruitful discussions with Dr. Soshi Kawai (Department of Aerospace Engineering, Tohoku University) and Dr. Shigeru Yonemura (Institute for Fluid Science, Tohoku University). This work was supported by JSPS ( Japan Society for the Promotion of Science ) KAKENHI Grant Numbers JP15J02622 and JP15K21767 . Numerical experiments were carried out on a vector supercomputer SX-ACE, Cybermedia Center, Osaka University.
Publisher Copyright:
© 2018 The Author(s)

PY - 2019/2/15

Y1 - 2019/2/15

N2 - 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.

AB - 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.

KW - Computational plasma physics

KW - Quadratic conservative scheme

KW - Relativistic Vlasov–Maxwell system

KW - Structure-preserving algorithm

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U2 - 10.1016/j.jcp.2018.10.041

DO - 10.1016/j.jcp.2018.10.041

M3 - Article

AN - SCOPUS:85057237702

VL - 379

SP - 32

EP - 50

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

ER -