  Efficient modeling of rarefied flow has drawn widespread interest for
practical engineering applications. In the present work, we proposed the Grad's
distribution function for 13 moments-based moment gas kinetic solver (G13-MGKS)
and the macroscopic governing equations are derived based on the moment
integral of discrete Boltzmann equation in the finite volume framework.
Numerical fluxes at the cell interface related to the macroscopic variables,
stress and heat flux can be reconstructed from the Boltzmann integration
equation at surrounding points of the cell interface directly, so the
complicated partial differential equations with tedious implementation of
boundary conditions in the moment method can be avoided. Meanwhile, the
explicit expression of numerical fluxes is proposed, which could release the
present solver the from the discretization and numerical summation in molecular
velocity space. To evaluate the Grad's distribution function for 13 moments in
the present framework, the G13-MGKS with the discrete and explicit form of
numerical fluxes are examined by several test cases covering the steady and
unsteady rarefied flows. Numerical results indicate that the G13-MGKS could
simulate continuum flows accurately and present reasonable prediction for
rarefied flows at moderate Knudsen number. Moreover, the tests of computations
and memory costs demonstrate that the present framework could preserve the
highly efficient feature.
