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Filtered Hyperbolic Moment Method for the Vlasov Equation
Di, Yana1,2; Fan, Yuwei3; Kou, Zhenzhong4; Li, Ruo5,6; Wang, Yanli7
AbstractIn this paper, we investigate the effect of the filter for the hyperbolic moment equations (HME) (Cai et al. in Commun Pure Appl Math 67(3):464-518, 2014; Cai et al. in SIAM J Sci Comput 35(6):A2807-A2831, 2013) of the Vlasov-Poisson equations and propose a novel quasi time-consistent filter to suppress the numerical recurrence effect. By taking properties of HME into consideration, the filter preserves a lot of physical properties of HME, including Galilean invariance and conservation of mass, momentum and energy. We present two viewpointscollisional viewpoint and dissipative viewpointto dissect the filter, and show that the filtered hyperbolic moment method can be treated as a solver of the Vlasov equation. Numerical simulations of the linear Landau damping and two stream instability demonstrate the effectiveness of the filter in restraining recurrence arising from particle streaming. Both the analysis and the numerical results indicate that the filtered method can capture the evolution of the Vlasov equation, even when phase mixing and filamentation dominate.
KeywordHyperbolic moment equations Vlasov equation Filter Landau damping Two-stream instability
Funding ProjectNatural Science Foundation of China[11501042] ; National Natural Science Foundation of China[9163030002]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000464896500012
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Document Type期刊论文
Corresponding AuthorWang, Yanli
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, NCMIS, LSEC, Beijing 100190, Peoples R China
2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
3.Stanford Univ, Dept Math, Stanford, CA 94305 USA
4.Chinese Acad Sci, Acad Math & Syst Sci, Beijing, Peoples R China
5.Peking Univ, LMAM, CAPT, Beijing, Peoples R China
6.Peking Univ, Sch Math Sci, Beijing, Peoples R China
7.Peking Univ, Coll Engn, Beijing, Peoples R China
Recommended Citation
GB/T 7714
Di, Yana,Fan, Yuwei,Kou, Zhenzhong,et al. Filtered Hyperbolic Moment Method for the Vlasov Equation[J]. JOURNAL OF SCIENTIFIC COMPUTING,2019,79(2):969-991.
APA Di, Yana,Fan, Yuwei,Kou, Zhenzhong,Li, Ruo,&Wang, Yanli.(2019).Filtered Hyperbolic Moment Method for the Vlasov Equation.JOURNAL OF SCIENTIFIC COMPUTING,79(2),969-991.
MLA Di, Yana,et al."Filtered Hyperbolic Moment Method for the Vlasov Equation".JOURNAL OF SCIENTIFIC COMPUTING 79.2(2019):969-991.
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