Energy-conserving discontinuous Galerkin methods for the Vlasov-Amp¨¨re system

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• 作者：Yingda Cheng ; Andrew J. Christlieb ; Xinghui Zhong
• 关键词：Vlasov&ndash ; Ampè ; re system ; Energy conservation ; Discontinuous Galerkin methods ; Landau damping ; Two-stream instability ; Bump-on-tail instability
• 刊名：Journal of Computational Physics
• 出版年：2014
• 出版时间：1 January, 2014
• 年：2014
• 卷：256
• 期：Complete
• 页码：630-655
• 全文大小：2844 K

文摘

In this paper, we propose energy-conserving numerical schemes for the Vlasov-Amp¨¨re (VA) systems. The VA system is a model used to describe the evolution of probability density function of charged particles under self consistent electric field in plasmas. It conserves many physical quantities, including the total energy which is comprised of the kinetic and electric energy. Unlike the total particle number conservation, the total energy conservation is challenging to achieve. For simulations in longer time ranges, negligence of this fact could cause unphysical results, such as plasma self heating or cooling. In this paper, we develop the first Eulerian solvers that can preserve fully discrete total energy conservation. The main components of our solvers include explicit or implicit energy-conserving temporal discretizations, an energy-conserving operator splitting for the VA equation and discontinuous Galerkin finite element methods for the spatial discretizations. We validate our schemes by rigorous derivations and benchmark numerical examples such as Landau damping, two-stream instability and bump-on-tail instability.