Conservative Discontinuous Galerkin/Hermite Spectral Method for the Vlasov-Poisson System  

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作  者:Francis Filbet Tao Xiong 

机构地区:[1]Institut de Mathématiques de Toulouse,UniversitéPaul Sabatier,Toulouse 31062,France [2]School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computing,Xiamen University,Xiamen 361005,Fujian Province,China

出  处:《Communications on Applied Mathematics and Computation》2022年第1期34-59,共26页应用数学与计算数学学报(英文)

基  金:the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014-2018 under Grant Agreement No.633053.;the Science Challenge Project(No.TZ2016002);the National Natural Science Foundation of China(No.11971025);the Natural Science Foundation of Fujian Province(No.2019J06002);the NSAF(No.U1630247)。

摘  要:We propose a class of conservative discontinuous Galerkin methods for the Vlasov-Pois-son system written as a hyperbolic system using Hermite polynomials in the velocity vari-able.These schemes are designed to be systematically as accurate as one wants with prov-able conservation of mass and possibly total energy.Such properties in general are hard to achieve within other numerical method frameworks for simulating the Vlasov-Poisson system.The proposed scheme employs the discontinuous Galerkin discretization for both the Vlasov and the Poisson equations,resulting in a consistent description of the distribu-tion function and the electric field.Numerical simulations are performed to verify the order of the accuracy and conservation properties.

关 键 词:Energy conserving Discontinuous Galerkin method Hermite spectral method Vlasov-Poisson 

分 类 号:O17[理学—数学]

 

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