  This paper derives transport equations for medium rarefied gases from the
Bhatnagar-Gross-Krook (BGK) model kinetic equation using a Hermite polynomial
approximation for the monoatomic gas distribution function. We apply the
Chapman-Enskog regularization method to Grad's velocity distribution function
that corresponds to his thirteen moment equation, extending these equations to
the third order of the Knudsen number. We show that the obtained set of Grad's
regularized thirteen moment equations is complete, and that all previously
obtained closures for Grad's thirteen moment equations are the sets of
truncated equations obtained in this paper. Using the truncated transport
equations may lead to losing accuracy in computing gas flows and heat transfer
in rarefied gases. The velocity distribution function for the resulting 13
regularized moment equations is presented.
