Berlin 2008 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 29: Poster II
DY 29.21: Poster
Thursday, February 28, 2008, 16:00–18:00, Poster C
From hyperbolic regularization to exact hydrodynamics via simple kinetic models — •Matteo Colangeli1, Martin Kröger1, and Ilya Karlin2 — 1Polymer Physics, ETH Zürich, Switzerland — 2Aerothermochemistry and Combustion Systems Lab, ETH Zürich, Switzerland
The derivation of hydrodynamics from a microscopic description is the classical problem of physical kinetics. The Chapman-Enskog method derives the solution from the Boltzmann Equation as a series in powers of Knudsen number. However, as demonstrated by Bobylev, even in the case of one-dimensional linear deviations from global equilibrium, the Burnett hydrodynamics violates the H-Theorem. We introduce a method to derive stable equations of linear hydrodynamics to any desired accuracy in Knudsen number. We first proceed with derivation from a thirteen Moments Grad System recovering and generalizing [1] the previous Bobylev result, including the proof of an H-theorem [2]. Further, we derive hydrodynamics from linearized Boltzmann Equation [3]. We demonstrate that stability of hydrodynamic equations arises as interplay between two basic features: dissipativity and hyperbolicity.
[1] M. Colangeli, I.V. Karlin, M. Kröger, From hyperbolic regularization to exact hydrodynamics for linearized Grad’s equations, Phys. Rev. E 75 (2007) 051204. [2] M. Colangeli, I.V. Karlin, M. Kröger, Hyperbolicity of exact hydrodynamics for three-dimensional linearized Grad’s equations, Phys. Rev. E 76 (2007) 022201. [3] M. Colangeli, M. Kröger, I.V. Karlin, "Eigen"-closure of linear Boltzmann equation from Invariant Manifold Theory (to be submitted).