scholarly journals On Symmetrical Methods for Charged Particle Dynamics

Symmetry ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1626
Author(s):  
Renxuan Tang ◽  
Dongfang Li
Keyword(s):  
Charged Particle ◽  
Auxiliary Variable ◽  
Particle Dynamics ◽  
High Order ◽  
High Order Accuracy ◽  
Order Accuracy ◽  
New Family ◽  
Ode System ◽  
Energy Conserving ◽  
Ode Systems

In this paper, we use the scalar auxiliary variable (SAV) approach to rewrite the charged particle dynamics as a new family of ODE systems. The systems own a conserved energy. It is shown that a family of symmetrical methods is energy-conserving for a new ODE system but may not be for the original systems. Moreover, the methods have high-order accuracy. Numerical results are given to confirm the theoretical findings.

scholarly journals High-Order Hybrid WCNS-CPR Scheme for Shock Capturing of Conservation Laws

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Jia Guo ◽  
Huajun Zhu ◽  
Zhen-Guo Yan ◽  
Lingyan Tang ◽  
Songhe Song
Keyword(s):  
Computational Cost ◽  
High Order ◽  
Shock Capturing ◽  
High Order Accuracy ◽  
Hybrid Technique ◽  
Hybrid Scheme ◽  
Order Accuracy ◽  
Order Of Accuracy ◽  
Reconstruction Scheme ◽  
High Gradients

By introducing hybrid technique into high-order CPR (correction procedure via reconstruction) scheme, a novel hybrid WCNS-CPR scheme is developed for efficient supersonic simulations. Firstly, a shock detector based on nonlinear weights is used to identify grid cells with high gradients or discontinuities throughout the whole flow field. Then, WCNS (weighted compact nonlinear scheme) is adopted to capture shocks in these areas, while the smooth area is calculated by CPR. A strategy to treat the interfaces of the two schemes is developed, which maintains high-order accuracy. Convergent order of accuracy and shock-capturing ability are tested in several numerical experiments; the results of which show that this hybrid scheme achieves expected high-order accuracy and high resolution, is robust in shock capturing, and has less computational cost compared to the WCNS.

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