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A numerical method for coupling the BGK model and Euler equations through the linearized Knudsen layer. (English) Zbl 1453.76149

Summary: 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 [Q. Li et al., ESAIM, Math. Model. Numer. Anal. 51, No. 5, 1583–1615 (2017; Zbl 1380.35006); Math. Comput. 86, No. 305, 1269–1301 (2017; Zbl 1360.35131)] 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 demonstrate that the linearization approach is promising.

MSC:

76M22 Spectral methods applied to problems in fluid mechanics
76M12 Finite volume methods applied to problems in fluid mechanics
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
76N15 Gas dynamics (general theory)
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References:

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