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In the current work we construct a multimolecule random process which leadsto the Boltzmann equation in the appropriate limit, and which is different fromthe deterministic real gas dynamics process. We approximate the statisticaldifference between the two processes via a suitable diffusion process, which isobtained in the multiscale homogenization limit. The resulting Boltzmannequation acquires a new spatially diffusive term, which subsequently manifestsin the corresponding fluid dynamics equations. We test the Navier-Stokes andGrad closures of the diffusive fluid dynamics equations in the numericalexperiments with the Couette flow for argon and nitrogen, and compare theresults with the corresponding Direct Simulation Monte Carlo (DSMC)computations. We discover that the full-fledged Knudsen velocity boundarylayers develop with all tested closures when the viscosity and diffusivity areappropriately scaled in the vicinity of the walls. Additionally, we find thatthe component of the heat flux parallel to the direction of the flow iscomparable in magnitude to its transversal component near the walls, and thatthe nonequilibrium Grad closure approximates this parallel heat flux with goodaccuracy.

Diffusive Boltzmann equation, its fluid dynamics, Couette flow and Knudsen layers