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A Quantified Model-Competition (QMC) mechanism for multi-scale flows isextracted from the integral (analytical) solution of the Boltzmann-BGK modelequation. In the QMC mechanism, the weight of the rarefied model and the weightof the continuum (aerodynamic/hydrodynamic) model are quantified. Then, aSimplified Unified Wave-Particle method (SUWP) is constructed based the on theQMC mechanism. In the SUWP, the stochastic particle method and the continuumNavier-Stokes method are combined together. Their weights are determined by theQMC mechanism quantitatively in every discrete cells of the computationaldomain. The validity and accuracy of the present numerical method are examinedusing a series of test cases including the high non-equilibrium shock wavestructure case, the unsteady Sod shock-tube case with a wide range of Knnumber, the hypersonic flow around the circular cylinder from thefree-molecular regime to the near continuum regime, and the viscous boundarylayer case. In the construction process of the present method, ananti-dissipation effect in the continuum mechanism is also discussed.

Simplified Unified Wave-Particle Method with Quantified Model-Competition Mechanism for Numerical Calculation of Multi-Scale Flows