  A Quantified Model-Competition (QMC) mechanism for multi-scale flows is
extracted from the integral (analytical) solution of the Boltzmann-BGK model
equation. In the QMC mechanism, the weight of the rarefied model and the weight
of the continuum (aerodynamic/hydrodynamic) model are quantified. Then, a
Simplified Unified Wave-Particle method (SUWP) is constructed based the on the
QMC mechanism. In the SUWP, the stochastic particle method and the continuum
Navier-Stokes method are combined together. Their weights are determined by the
QMC mechanism quantitatively in every discrete cells of the computational
domain. The validity and accuracy of the present numerical method are examined
using a series of test cases including the high non-equilibrium shock wave
structure case, the unsteady Sod shock-tube case with a wide range of Kn
number, the hypersonic flow around the circular cylinder from the
free-molecular regime to the near continuum regime, and the viscous boundary
layer case. In the construction process of the present method, an
anti-dissipation effect in the continuum mechanism is also discussed.
