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Constructing Poisson and Dissipative Brackets of Mixtures by using Lagrangian-to-Eulerian Transformation

Published online by Cambridge University Press:  05 May 2011

K.-C. Chen
K.-C. Chen*
Affiliation:
Institute of Applied Mechanics, National Taiwan University, Taipei, Taiwan 10617, R.O.C.
*
* Professor, corresponding author
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Abstract

This paper aims to construct the bracket formalism of mixture continua by using the method of Lagrangian- to-Eulerian (LE) transformation. The LE approach first builds up the transformation relations between the Eulerian state variables and the Lagrangian canonical variables, and then transforms the bracket in Lagrangian form to the bracket in Eulerian form. For the conservative part of the bracket formalism, this study systematically generates the noncanonical Poisson brackets of a two-component mixture. For the dissipative part, we deduce the Eulerian-variable-based dissipative brackets for viscous and diffusive mechanisms from their Lagrangian-variable-based counterparts. Finally, the evolution equations of a micromorphic fluid, which can be treated as a multi-component mixture, are derived by constructing its Poisson and dissipative brackets.

Keywords

Noncanonical poisson bracketDissipative bracketLagrangian-to-Eulerian transformationMicromorphic fluid
Type
Articles
Information
Journal of Mechanics , Volume 26 , Issue 2 , June 2010 , pp. 219 - 228
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2010

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