In this work, the Navier-Stokes (NS) solver is combined with the Direct
simulation Monte Carlo (DSMC) solver in a direct way, under the wave-particle
formulation [J. Comput. Phys. 401, 108977 (2020)]. Different from the classical
domain decomposition method with buffer zone for overlap, in the proposed
direct unified wave-particle (DUWP) method, the NS solver is coupled with DSMC
solver on the level of algorithm. Automatically, in the rarefied flow regime,
the DSMC solver leads the simulation, while the NS solver leads the continuum
flow simulation. Thus advantages of accuracy and efficiency are both taken. At
internal flow regimes, like the transition flow regime, the method is accurate
as well because a kind of mesoscopic modeling is proposed in this work, which
gives the DUWP method the multi-scale property. Specifically, as to the
collision process, at t<Ο, it is supposed that only single collision
happens, and the collision term of DSMC is just used. At t>Ο, it is
derived that 1βΟ/Ξt of particles should experience multiple
collisions, which will be absorbed into the wave part and calculated by the NS
solver. Then the DSMC and NS solver can be coupled in a direct and simple way,
bringing about multi-scale property. The governing equation is derived and
named as multi-scale Boltzmann equation. Different from the original
wave-particle method, in the proposed DUWP method, the wave-particle
formulation is no more restricted by the Boltzmann-BGK type model and the
enormous research findings of DSMC and NS solvers can be utilized into much
more complicated flows, like the thermochemical non-equilibrium flow. In this
work, one-dimensional cases in monatomic argon gas are preliminarily tested,
such as shock structures and Sod shock tubes