# A Numerical method for coupling the BGK model and Euler equation through the linearized Knudsen layer

Journal Article

The Bhatnagar-Gross-Krook (BGK) model, a simplification of the Boltzmann equation, in the absence of boundary effect, converges to the Euler equation when the Knudsen number is small. In practice, however, Knudsen layers emerge at the physical boundary, or at the interfaces between the two regimes. We model the Knudsen layer using a half-space kinetic equation, and apply a half-space numerical solver [ESAIM: M2AN 51 (2017) 1583-1615] [Math. Comp. 86 (2017), 1269-1301] to quantify the transition between the kinetic to the fluid regime. A full domain numerical solver is developed based on domain-decomposition method, with the Euler solver and kinetic solver applied on the appropriate parts of the domain and connected through the half-space solver.

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### Cited Authors

- Chen, H; Li, Q; Lu, J