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This article is cited in 5 scientific papers (total in 5 papers)
The Method of Singular Equations in Boundary Value Problems in Kinetic Theory
A. V. Latyshev, A. A. Yushkanov Moscow State Region University
Abstract:
We develop a new effective method for solving boundary value problems in kinetic theory. The method permits solving boundary value problems for mirror and diffusive boundary conditions with an arbitrary accuracy and is based on the idea of reducing the original problem to two problems of which one has a diffusion boundary condition for the reflection of molecules from the wall and the other has a mirror boundary condition. We illustrate this method with two classical problems in kinetic theory: the Kramers problem (isothermal slip) and the thermal slip problem. We use the Bhatnagar–Gross–Krook equation (with a constant collision frequency) and the Williams equation (with a collision frequency proportional to the molecular velocity).
Keywords:
boundary value problem, kinetic equation, Kramers problem, thermal slip problem, isothermal slip coefficient, thermal slip coefficient.
Received: 28.09.2004 Revised: 26.11.2004
Citation:
A. V. Latyshev, A. A. Yushkanov, “The Method of Singular Equations in Boundary Value Problems in Kinetic Theory”, TMF, 143:3 (2005), 437–454; Theoret. and Math. Phys., 143:3 (2005), 854–869
Linking options:
https://www.mathnet.ru/eng/tmf1824https://doi.org/10.4213/tmf1824 https://www.mathnet.ru/eng/tmf/v143/i3/p437
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