We study the nonlinear stability of the Boltzmann equation in the 3-dimensional periodic box with size 1/ε of each side, where 0 < ε 1 is the Knudsen number. The initial perturbation is not necessary smooth. The convergence rate is algebraic for small time region and exponential for large time region. Moreover, the algebraic rate is optimal and the exponential rate depends on the size of the do...

Classical continuummethods break down for rarefied gas flows inmicro-channels. Twononcontinuumhydrodynamicmodels are investigated here: compressible Korteweg fluid-like andBiVelocity (VolumeDiffusion) hydrodynamicmodels. The pressure driven rarefied gasflow in a rectangularmicro-channel in thewhole range of Knudsen number is numerically considered. The Kortewegmodel shows improved results in co...

Classical continuummethods break down for rarefied gas flows inmicro-channels. Twononcontinuumhydrodynamicmodels are investigated here: compressible Korteweg fluid-like andBiVelocity (VolumeDiffusion) hydrodynamicmodels. The pressure driven rarefied gasflow in a rectangularmicro-channel in thewhole range of Knudsen number is numerically considered. The Kortewegmodel shows improved results in co...

Vapor jets of DNA and RNA bases (adenine, cytosine, thymine, and uracil) from an oven with a capillary exit have been studied in the intermediate regime between molecular and viscous flow corresponding to Knudsen numbers in the range 0.1 < Kn < 10. The temperature control method ensured stationary flow. Assuming the Knudsen hypothesis, the pressure of sublimated molecules in the oven was determ...

This paper presents molecular dynamics simulations of the Couette flow a rarefied gas between liquid and wall boundaries and, in particular, investigates boundary conditions for Boltzmann equation at interface. The simulation results various Knudsen numbers show that slip velocity decreases increases smooth as number increases, indicating profile is asymmetric. One reason this backscattering, w...

Hypersonic rarefied-gas flows near two side-by-side plates and cylinders, a plate and cylinder over a plane surface, and a plate behind a cylinder in argon and nitrogen have been studied numerically using the direct simulation Monte-Carlo technique under the transition rarefied-gas-flow regime conditions at Knudsen numbers from 0.004 to 10. Strong influences of the geometrical factor (the ratio...

A linear kinetic equation for heat transfer is solved by means of the method of moments. The moment equations are solved with Maxwelltype boundary conditions for steady state energy transport. The results exhibit marked Knudsen boundary layers. The accuracy of the description is examined, and it is shown that already a relatively small number of moments can give satisfactory resolution of Knuds...

A modular particle-continuum (MPC) numerical method is used to simulate steady-state hypersonic flows which exhibit local regions of non-equilibrium embedded within mainly continuum flow fields. The MPC method loosely couples direct simulation Monte Carlo (DSMC) and Navier-Stokes (NS) methods which operate in different regions, use different mesh densities, and are updated using different sized...

Shale gas flow at the pore scale is very challenging to simulate due high Knudsen numbers (Kn), low speeds and complicated geometries. The direct simulation BGK (DSBGK) method discrete velocity (DVM) are promising methods three-dimensional (3D) flows in shale rock. As grid-convergence accuracy computational cost highly depend on spatial molecular grids, here we present a rigorous study of perfo...