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In order to describe a two-dimensional flow of a dilute, hard sphere gas in the transitional regime, the DSMC numerical method (direct simulation Monte Carlo) is used to solve the Boltzmann equation in the corresponding case. To do this, the gas is enclosed under the effect of a gravity field in a square cavity whose walls have equal temperatures at first, which then change according to a temperature gradient in the vertical direction. To simplify the study and to use convenient boundary conditions, the surrounding gas of the cavity is considered to be Maxwellian. The behaviour of the system can be inferred from the profiles of density, temperature, pressure and heat flux, and is then compared with previous theoretical models.

DSMC method for a two-dimensional flow with a gravity field in a square cavity