Probabilistic approach for rarefied gas dynamics: Linearized couette flow

摘要

In the present paper, extending a new probabilistic approach for radiative transfer [1] to the linear version of the Boltzmann equation based on the Krook kinetic model, an integral equation for the one-dimensional reflection function R(τ; u, u0) is derived from the Chapman-Kolmogoroff equation in somewhat modified form. It is assumed that the joint probability of the molecular diffuse reflection at the moving wall has the Markovian character of the multiple scattering of particles. Then, the requisite perturbation velocity distribution at the moving wall is expressed in terms of the integrated R-function. Furthermore, it is shown that, by verifying the reciprocity principle for R(τ; u, u0)ēu02, the integral equation for the reflection function S(τ; u, u0) is derived from the integral equation for R-function in the case of the linearized Couette flow.