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A finite element solution technique for the Boltzmann equation

Published online by Cambridge University Press:  29 March 2006

T. Taz Bramlette  and
Robert H. Mallett
T. Taz Bramlette
Affiliation:
Bell Aerospace Company Division of Textron Inc., Buffalo, New York 14240.
Robert H. Mallett
Affiliation:
Bell Aerospace Company Division of Textron Inc., Buffalo, New York 14240.
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Abstract

A new method is presented for solution of the Boltzmann equation governing the dynamic behaviour of gases. The essence of the method is idealization of the problem domain into subdomains called finite elements. Then, the Galerkin assumed-mode technique is employed as the basis for discretization of the individual finite elements and also for the assembly of the resulting algebraic models for these finite elements to form an algebraic model for the complete problem. The procedure is cast in a systematic matrix notation that makes evident the broad application potential of the analysis method. An illustrative application is presented for the problem of one-dimensional, linearized Couette flow. Numerical predictions of macroscopic flow velocity and viscous shear stress based upon the subject finite element method are compared with alternative analytical and numerical results. Special attributes of the finite element method are discussed in the context of this example problem. Applications to practical problems governed by generalized forms of the Boltzmann equation are projected on the basis of concepts established herein.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 42 , Issue 1 , 4 June 1970 , pp. 177 - 191
Copyright
© 1970 Cambridge University Press

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