Dr. Takayuki UMEDA
Associate Professor

Center for Integrated Data Science
Institute for Space-Earth Environmental Research
Nagoya University
Nagoya, Aichi 464-8601, JAPAN

Email: taka.umeda @ nagoya-u.jp
Tel: +81-52-747-6351
Fax: +81-52-747-6334


Vlasov Code Simulations

*This work has been supported by
  • Grant-In-Aid (KAKENHI) for Young Scientists (Start Up) No.19840024 "Study of revolutionary Vlasov simulation techniques"
  • Grant-In-Aid (KAKENHI) for Young Scientists (B) No.21740352 "Study of Vlasov simulation techniques for next-generation supercomputers"
  • Grant-In-Aid (KAKENHI) for Young Scientists (B) No.23740367 "Study of cross-scale coupling in space plasma via large-scale Vlasov simulations"
  • Grant-In-Aid (KAKENHI) for Challenging Exploratory Research No.25610144 "Six-dimensional Vlasov simulation"
  • Numerical Code for Educational Purpose

    The numerical code has been developed for the 11th International School / Symposium for Space Simulations (ISSS-11) and modified for 13th International School / Symposium for Space Simulations (ISSS-13).

    Application Examples of Multi-dimensional simulations

    Various physical processes in space plasma have been simulated with the massively-parallel multi-dimensional Vlasov code.

  • Magnetic Reconnection
    • T. Umeda, K. Togano, and T. Ogino, Two-dimensional full-electromagnetic Vlasov code with conservative scheme and its application to magnetic reconnection, Comput. Phys. Commun., Vol.180, 365-374, 2009.
    • T. Umeda, K. Togano, and T. Ogino, Structures of diffusion regions in collisionless magnetic reconnection, Phys. Plasmas, Vol.17, 052103, 2010.
    • S. Zenitani and T. Umeda, Some remarks on the diffusion regions in magnetic reconnection, Phys. Plasmas, Vol.21, 034503, 2014.

  • Kelvin-Helmholtz Instability
    • T. Umeda, J. Miwa, Y. Matsumoto, T. K. M. Nakamura, K. Togano, K. Fukazawa, and I. Shinohara, Full electromagnetic Vlasov code simulation of the Kelvin-Helmholtz instability, Phys. Plasmas, Vol.17, 052311, 2010.
    • T. Umeda, S. Ueno, and T. K. M. Nakamura, Ion kinetic effects to nonlinear processes of the Kelvin-Helmholtz instability, Plasma Phys. Contr. Fusion, Vol.56, 075006, 2014.

  • Rayleigh-Taylor instability
    • T. Umeda and Y. Wada, Secondary instabilities in the collisionless Rayleigh-Taylor instability: Full kinetic simulation, Phys. Plasmas, Vol.23, 112117, 2016.
    • T. Umeda and Y. Wada, Non-MHD effects in the nonlinear development of the MHD-scale Rayleigh-Taylor instability, Phys. Plasmas, Vol.24, 072307, 2017.

  • Interaction between plasma wind and bodies (planets/satellites)
    • T. Umeda, T. Kimura, K. Togano, K. Fukazawa, Y. Matsumoto, T. Miyoshi, N. Terada, T. K. M. Nakamura, and T. Ogino, Vlasov simulation on the interaction between solar wind and a dielectric body, Phys. Plasmas, Vol.18, 012908, 2011.
    • T. Umeda, Effect of ion cyclotron motion on the structure of wakes: A Vlasov simulation, Earth Planets Space, Vol.64, 231-236, 2012.
    • T. Umeda and Y. Ito, Entry of solar-wind ions into the wake of a small body with a magnetic anomaly: A global Vlasov simulation, Planet. Space Sci., Vol.93-94, 35-40, 2014.
    • T. Umeda and K. Fukazawa, A high-resolution global Vlasov simulation of a small dielectric body with a weak intrinsic magnetic field on the K computer, Earth Planets Space, Vol.67, 49, 2015.
    Two-trillion-grids simulation on the K computer

    Numerical Schemes

  • Vlasov equation
  • The Vlasov equation   \( \frac{\partial f_s}{\partial t} + \mathbf{v}\cdot \frac{\partial f_s}{\partial \mathbf{x}} + \frac{q_s}{m_s}\left( \mathbf{E} + \mathbf{v} \times \mathbf{B} \right) \cdot \frac{\partial f_s}{\partial \mathbf{v}} = 0 \)   is separated into the following three sub-equations based on the operator splitting.

    \( \frac{\partial f_s}{\partial t} + \mathbf{v}\cdot \frac{\partial f_s}{\partial \mathbf{x}} = 0 \)

    \( \frac{\partial f_s}{\partial t} + \frac{q_s}{m_s}\mathbf{E} \cdot \frac{\partial f_s}{\partial \mathbf{v}} = 0 \)

    \( \frac{\partial f_s}{\partial t} + \frac{q_s}{m_s}\left( \mathbf{v} \times \mathbf{B} \right) \cdot \frac{\partial f_s}{\partial \mathbf{v}} = 0 \)

    The first two advection equations are solved with a multi-dimensional unsplit advection method, while the third rotation equation is solved with the back-substitution method. For solving these equations, a high-order conservative and non-oscillatory scheme is used, which exactly satisfies the continuity equation for charge   \( \frac{\partial \rho}{\partial t} + \nabla \cdot \mathbf{J} = 0 \).
    • T. Umeda, K. Togano, and T. Ogino, Two-dimensional full-electromagnetic Vlasov code with conservative scheme and its application to magnetic reconnection, Comput. Phys. Commun., Vol.180, 365-374, 2009.
    • H. Schmitz and R. Grauer, Comparison of time splitting and backsubstitution methods for integrating Vlasov's equation with magnetic fields, Comput. Phys. Commun., Vol.175, 86-92, 2006.
    • T. Umeda, A conservative and non-oscillatory scheme for Vlasov code simulations, Earth Planets Space, Vol.60, 773-779, 2008.
    • T. Umeda, Y. Nariyuki, and D. Kariya, A non-oscillatory and conservative semi-Lagrangian scheme with fourth-degree polynomial interpolation for solving the Vlasov equation, Comput. Phys. Commun., Vol.183, 1094-1100, 2012.

  • Maxwell equations
  • The Maxwell equations are solved with the Finite-Difference Time-Domain (FDTD) method based on the Yee grid system, as standard particle-in-cell codes do.
    • K.S. Yee, Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media, IEEE Trans. Antennas Propag., Vol.AP-14, 302-307, 1966.