Energy-conserving discontinuous Galerkin methods for the Vlasov-Maxwell system

JOURNAL OF COMPUTATIONAL PHYSICS

卷:279

Article

Cheng, Yingda¹  Christlieb, Andrew J.¹  Zhong, Xinghui¹ 

[1] Michigan State Univ, Dept Math, E Lansing, MI 48824 USA

关键词: Vlasov-Maxwell system;    Energy conservation;    Symplectic integrators;    Discontinuous Galerkin methods;    Streaming Weibel instability;   

DOI  :  10.1016/j.jcp.2014.08.041

来源: Elsevier

【 摘 要 】

In this paper, we generalize the idea in our previous work for the Vlasov-Ampere (VA) system (Y. Cheng, A. J. Christlieb, and X. Zhong (2014) [10]) and develop energy-conserving discontinuous Galerkin (DG) methods for the Vlasov-Maxwell (VM) system. The VM system is a fundamental model in the simulation of collisionless magnetized plasmas. Compared to Y. Cheng, A. J. Christlieb, and X. Zhong (2014) [10], additional care needs to be taken for both the temporal and spatial discretizations to achieve similar type of conservation when the magnetic field is no longer negligible. Our proposed schemes conserve the total particle number and the total energy at the same time, therefore can obtain accurate and physically relevant numerical solutions. The main components of our methods include second order and above, explicit or implicit energy-conserving temporal discretizations, and DG methods for Vlasov and Maxwell's equations with carefully chosen numerical fluxes. Benchmark numerical tests such as the streaming Weibel instability are provided to validate the accuracy and conservation of the schemes. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free