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A study on the non-equilibrium statistical mechanics of particle methods based on Hamiltonian mechanics

Research Project

Project/Area Number 23540166
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionWaseda University

Principal Investigator

SUZUKI Yukihito  早稲田大学, 理工学術院, 主任研究員 (90596975)

Co-Investigator(Renkei-kenkyūsha) SHIBATA Yoshihiro  早稲田大学, 理工学術院, 教授 (50114088)
YOSHIMURA Hiroaki  早稲田大学, 理工学術院, 教授 (40247234)
ITO Kimihisa  早稲田大学, 理工学術院, 教授 (10159866)
Project Period (FY) 2011-04-28 – 2015-03-31
Project Status Completed (Fiscal Year 2014)
Budget Amount *help
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywords粒子法 / ハミルトン力学 / 非平衡熱力学 / 連続体力学 / 解析力学 / 非平衡統計力学
Outline of Final Research Achievements

A particle method based on the GENERIC formalism which is a theoretical framework for non-equilibrium thermodynamics has been studied. Indeed, a particle method based on the Poisson bracket defined on the state space of the Eulerian description of fluid flow has been developed and some numerical experiments have been done. In addition, the two-dimensional vorticity equation has been formulated within the GENERIC formalism and discretized using the discrete variational derivative method. The thus-obtained numerical method preserves or dissipates the kinetic energy and enstrophy depending on whether the flow is inviscid or viscid.

Report

(5 results)
  • 2014 Annual Research Report   Final Research Report ( PDF )
  • 2013 Research-status Report
  • 2012 Research-status Report
  • 2011 Research-status Report
  • Research Products

    (1 results)

All 2014

All Presentation (1 results)

  • [Presentation] 離散変分法による渦度方程式の数値解法2014

    • Author(s)
      鈴木幸人,大繩将司,及川一誠
    • Organizer
      日本応用数理学会2014年度年会
    • Place of Presentation
      東京
    • Year and Date
      2014-09-03
    • Related Report
      2014 Annual Research Report

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Published: 2011-08-05   Modified: 2019-07-29  

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