A Numerical method for coupling the BGK model and Euler equation through the linearized Knudsen layer
For researchers simulating gas flows with mixed kinetic and continuum regimes, this provides a practical coupling method, though it is incremental and lacks analytical justification.
This work develops a domain-decomposition numerical method coupling the BGK kinetic model with the Euler equations by modeling Knudsen layers via a half-space kinetic solver. Numerical results show the linearization approach is promising for capturing the transition between kinetic and fluid regimes.
The Bhatnagar-Gross-Krook (BGK) model, a simplification of the Boltzmann equation, in the absence of boundary effect, converges to the Euler equations 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 with a domain-decomposition approach, where we apply the Euler solver and kinetic solver on the appropriate subdomains and connect them via the half-space solver. In the nonlinear case, linearization is performed upon local Maxwellian. Despite the lack of analytical support, the numerical evidence nevertheless demonstrates that the linearization approach is promising.