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This study proposes a scattering database method to model gas–solid interaction based on a database of distributions of scattering velocity obtained by a molecular dynamics simulation. The proposed method is used as the boundary condition in the direct simulation Monte Carlo method to simulate hypersonic flow over a rounded wedge at different Knudsen numbers (Kn). The effects of different wall models [e.g., the scattering database method and the Cercignani–Lampis–Lord (CLL) model] on the flow simulation were compared and analyzed. When Kn ≥ 1, the results based on the CLL model are evidently different from those of the scattering database model, where this difference increases with the degree of rarefication of flow. The mechanism of this discrepancy is such that when the flow is rarefied, a large number of freestream molecules from the far-field directly collide with the wall. In particular, near the stagnation point, the tangential reflection kinetic energy of freestream molecules is amplified due to the conversion of their normal incident kinetic energy. The scattering feature of this conversion is challenging to reproduce based on the theoretical framework of the CLL model. Still, a specific local parameter can describe the ratio of this conversion. Therefore, compared with the traditional wall model, the scattering database method can show more detailed scattering features and, hence, could be a promising tool for the study of gas–solid interaction in hypersonic rarefied flow.

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Multi-fluid flows involving shock-accelerated inhomogeneities and shock-induced instability play essential roles in a wide variety of problems including, but not limited to, supersonic combustion [1], inertial confinement fusion [2], and supernova explosion [3]. Numerical simulations of these complex flows prove to be challenging in the presence of moving and deformable material interfaces, especially for fluids with large differences in their densities or thermodynamic properties. Therefore, a discontinuity-capturing, mass-conserving, and positivity-preserving scheme is desirable for compressible multi-fluid simulations.

The previous chapter has shown that the necessary numerical dissipation can be introduced in 1D CESE schemes through either a central or upwind approach.