A hybrid finite-element/finite-volume node-pair discretization of conservation laws is reformulated in terms of a Bhatnagar–Gross–Krook kinetic scheme to address flows from the continuum up to the transitional regime in a seamless fashion. Integrals of the particle distribution function from the kinetic theory of gases are adopted to compute the numerical fluxes along the boundary of each control volume. Flow features typical of the transitional regime like velocity and temperature slip condition at solid walls are automatically assured by the kinetic formulation of the node-pair boundary conditions. Exemplary two-dimensional numerical experiments ranging from continuum flows up to the transitional regime are presented.
Fossati, M., Guardone, A., Vigevano, L., & Xu, K. (2013). A kinetic node-pair formulation for two-dimensional flows from continuum to transitional regime. AIAA Journal, 51(4), 784-796. https://doi.org/10.2514/1.J051545