Slip Boundary Conditions for the Compressible Navier–Stokes Equations

Kazuo Aoki (1) , Céline Baranger (2) , Masanari Hattori (1) , Shingo Kosuge (1) , Giorgio Martalo (3) , Julien Mathiaud (2) , Luc Mieussens (4, 3)

1 Department of Mechanical Engineering and Science
2 CESTA - Centre d'études scientifiques et techniques d'Aquitaine
3 CARDAMOM - Certified Adaptive discRete moDels for robust simulAtions of CoMplex flOws with Moving fronts
4 IMB - Institut de Mathématiques de Bordeaux

The slip boundary conditions for the compressible Navier–Stokes equations are derived systematically from the Boltzmann equation on the basis of the Chapman–Enskog solution of the Boltzmann equation and the analysis of the Knudsen layer adjacent to the boundary. The resulting formulas of the slip boundary conditions are summarized with explicit values of the slip coefficients for hard-sphere molecules as well as the Bhatnagar–Gross–Krook (BGK) model. These formulas, which can be applied to specific problems immediately, help to prevent the use of often used slip boundary conditions that are either incorrect or without theoretical basis.

Mots clés: Navier–Stokes equations; Boltzmann equation; Moving boundary problems; Knudsen layer; Slip boundary conditions

Domaines: Mécanique des fluides [physics.class-ph]; Equations aux dérivées partielles [math.AP]

Kazuo Aoki, Céline Baranger, Masanari Hattori, Shingo Kosuge, Giorgio Martalo, et al.. Slip Boundary Conditions for the Compressible Navier–Stokes Equations. Journal of Statistical Physics, 2017, 169 (4), pp.744-781. ⟨10.1007/s10955-017-1886-8⟩. ⟨hal-01634602⟩