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

doi:10.1007/s42967-020-00089-z

Communications on Applied Mathematics and Computation ›› 2022, Vol. 4 ›› Issue (1): 34-59.doi: 10.1007/s42967-020-00089-z

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

Francis Filbet¹, Tao Xiong²

1 Institut de Mathématiques de Toulouse, Université Paul Sabatier, Toulouse 31062, France;
2 School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientifc Computing, Xiamen University, Xiamen 361005, Fujian Province, China

Received:2020-04-06 Revised:2020-07-07 Online:2022-03-20 Published:2022-03-01
Contact: Tao Xiong, Francis Filbet E-mail:txiong@xmu.edu.cn;francis.flbet@math.univ-toulouse.fr
Supported by:
Francis Filbet is supported by the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014-2018 under Grant Agreement No. 633053. The views and opinions expressed herein do not necessarily refect those of the European Commission. T. Xiong acknowledges support by the Science Challenge Project (No. TZ2016002), the National Natural Science Foundation of China (No. 11971025), the Natural Science Foundation of Fujian Province (No. 2019J06002), and the NSAF (No. U1630247). This work started when Francis Filbet visited the Tianyuan Mathematical Center in Southeast China at Xiamen University in June 2019 for a research group discussion. The author would like to thank the Tianyuan Mathematical Center for its hospitality.

Abstract

Abstract: We propose a class of conservative discontinuous Galerkin methods for the Vlasov-Poisson system written as a hyperbolic system using Hermite polynomials in the velocity variable. These schemes are designed to be systematically as accurate as one wants with provable 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 distribution function and the electric feld. Numerical simulations are performed to verify the order of the accuracy and conservation properties.

Key words: Energy conserving, Discontinuous Galerkin method, Hermite spectral method, Vlasov-Poisson

CLC Number:

Francis Filbet, Tao Xiong. Conservative Discontinuous Galerkin/Hermite Spectral Method for the Vlasov-Poisson System[J]. Communications on Applied Mathematics and Computation, 2022, 4(1): 34-59.

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References

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

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