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Trimodal approximate solutions of the non‐linear Boltzmann equation
Author(s) -
Gordevsky V. D.
Publication year - 1998
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(19981110)21:16<1479::aid-mma5>3.0.co;2-i
Subject(s) - mathematics , boltzmann equation , knudsen number , metric (unit) , zero (linguistics) , mathematical analysis , boltzmann constant , linear equation , class (philosophy) , physics , thermodynamics , linguistics , operations management , philosophy , artificial intelligence , computer science , economics
Approximate solutions of the non‐linear Boltzmann equation, which have the structure of the linear combination of three global Maxwellians with arbitrary hydrodynamical parameters, are considered. Some sufficient conditions which allow the error between the left‐ and the right‐hand sides of the equation tend to zero, and which are calculated either in the mixed metric or in the pure integral metric, are obtained. The class of the distributions, which minimized this error for the arbitrary Knudsen number, is found. © 1998 B. G. Teubner Stuttgart—John Wiley & Sons, Ltd.