期刊
MULTISCALE MODELING & SIMULATION
卷 6, 期 1, 页码 53-69出版社
SIAM PUBLICATIONS
DOI: 10.1137/060654700
关键词
coarse graining; dynamic systems; Poisson brackets; dissipative brackets; general equation for the nonequilibrium reversible-irreversible coupling structure; nonequilibrium thermodynamics; hydrodynamics; Grad's moment equations
We employ systematic coarse graining techniques to derive hydrodynamic equations from Grad's ten-moment equations. The coarse graining procedure is designed such that it manifestly preserves the thermodynamic structure of the equations. The relevant thermodynamic structure and the coarse graining recipes suggested by statistical mechanics are described in detail and are illustrated by the example of hydrodynamics. A number of mathematical challenges associated with structure-preserving coarse graining of evolution equations for thermodynamic systems as a generalization of Hamiltonian dynamic systems are presented. Coarse graining is a key step that should always be considered before attempting to solve an equation.
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