Unique moment set from the order of magnitude method

Henning Struchtrup

doi:10.3934/krm.2012.5.417

Article Contents

2012, Volume 5, Issue 2: 417-440. Doi: 10.3934/krm.2012.5.417

This issue Previous Article Large-time decay of the soft potential relativistic Boltzmann equation in $\mathbb{R}^3_x$ Next Article

Unique moment set from the order of magnitude method

Henning Struchtrup^1,

1.
Department of Mechanical Engineering, University of Victoria, Victoria BC V8W 3P6

Received: October 31, 2011

Revised: January 31, 2012

Published: May 2012

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Abstract

The order of magnitude method [Struchtrup, Phys. Fluids 16, 3921-3934 (2004)] is used to construct a unique moment set for 1-D transport with scattering. Simply speaking, the method uses a series of leading order Chapman-Enskog expansions in the Knudsen number to construct the moments such that the number of moments at a given Chapman-Enskog order is minimal. For isotropic scattering, when one begins with monomials for the moments, the method constructs step by step moments of the Legendre polynomials. For anisotropic scattering, however, it constructs moments of new polynomials relevant for the particular scattering mechanism. All terms in the final moment equations are scaled by powers of the Knudsen number, which gives an easy handle to model reduction.

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Mathematics Subject Classification: Primary: 76P05, 82B40; Secondary: 53C35.

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