Unique moment set from the order of magnitude method

Pages: 417 - 440, Volume 5, Issue 2, June 2012

doi:10.3934/krm.2012.5.417       Abstract        References        Full Text (384.0K)       Related Articles

Henning Struchtrup - Department of Mechanical Engineering, University of Victoria, Victoria BC V8W 3P6, Canada (email)

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.

Keywords:  Kinetic theory of gases, moment method, Chapman-Enskog method, Knudsen number approximation, order of magnitude method.
Mathematics Subject Classification:  Primary: 76P05, 82B40; Secondary: 53C35.

Received: November 2011;      Revised: February 2012;      Published: April 2012.

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