A Lagrangian variational formulation for nonequilibrium thermodynamics. Part II: Continuum systems

JOURNAL OF GEOMETRY AND PHYSICS

卷:111

Article

Gay-Balmaz, Francois¹  Yoshimura, Hiroaki² 

[1] Ecole Normale Super Paris, CNRS, LMD, IPSL, 24 Rue Lhomond, F-75005 Paris, France

[2] Waseda Univ, Sch Sci & Engn, Shinjuku Ku, Tokyo 1698555, Japan

关键词: Lagrangian formulation;    Nonequilibrium thermodynamics;    Variational formulation;    Nonholonomic constraints;    Irreversible processes;    Continuum systems;   

DOI  :  10.1016/j.geomphys.2016.08.019

来源: Elsevier

【 摘 要 】

Part I of this paper introduced a Lagrangian variational formulation for nonequilibrium thermodynamics of discrete systems. This variational formulation extends Hamilton's principle to allow the inclusion of irreversible processes in the dynamics. The irreversibility is encoded into a nonlinear nonholonomic constraint given by the expression of entropy production associated to all the irreversible processes involved. In Part II, we develop this formulation for the case of continuum systems by extending the setting of Part I to infinite dimensional nonholonomic Lagrangian systems. The variational formulation is naturally expressed in the material representation, while its spatial version is obtained via a nonholonomic Lagrangian reduction by symmetry. The theory is illustrated with the examples of a viscous heat conducting fluid and its multicomponent extension including chemical reactions and mass transfer. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

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