Computation of unstable rarefied gas flow in channels with different scattering functions

Abstract

Obtained in our previous analytical and numerical investigations cascade of bifurcations is simulated numerically for different scattering functions generalizing the ray-diffuse reflection of gas particles from the surface. Analytical solutions we obtained earlier for the ray reflection which means only one determined velocity of reflected from the walls gas atoms, generally different from the specular reflection. Monte Carlo method is applied to simulate gas flows in channels for ray-diffuse and more general models of scattering functions V. The nonlinear iterative equation describing a rarefied gas flow in a long channel becomes unstable in some regions of corresponding parameters of V (it means the sensitivity to boundary conditions). The values of the parameters are found from analytical approximations in these regions. Numerical results show that the chaotic behavior of the nonlinear dynamic system corresponds to strange attractors and distinguishes clearly from Maxwellian distribution and from the equilibrium on the whole. In the regions of instability (as the dimension of the attractor increases) the search for a corresponding state requires a lot more computation time and a lot of data (the amount of data required increases exponentially with embedding dimension). Therefore the main complication in the computation is reducing as well the computing time as the amount of data to find a suitably close solution. To reduce the computing time our analytical results are applied. Flow conditions satisfying the requirements to the experiment are indicated where the instability of considered type can be detected.