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

2014 Fiscal Year Final Research Report

• Project/Area Number: 23540166
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Waseda 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
• Keywords: 粒子法 / ハミルトン力学 / 非平衡熱力学

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.

Free Research Field

数値流体力学