Macroscopic transport equations for rarefied gas flows

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Principles of Multiscale Modeling (2012, background): “Grad’s 13-moment model is a primarily example of this kind [20, 38].”
Numerical methods for kinetic equations* (2014, methodology): “We refer to Struchtrup (2005) for alternative approaches that avoid some of the shortcomings of the classical high-order closures.”
A high-order moment approach for capturing non-equilibrium phenomena in the transition regime (2009, methodology): “From the Boltzmann equation, it is possible to obtain governing equations for mijk , Rij and for Maxwell molecules as follows (Struchtrup 2005): ∂mijk ∂t + ∂ulmijk ∂xl + ∂φijkl ∂xl = −3 2 p μ mijk − 3p ∂(σ〈ij /ρ) ∂xk〉 + Mijk, (16) ∂Rij ∂t + ∂ukRij ∂xk + ∂ψijk ∂xk = −7 6 p μ Rij − 28 5 p ∂(q〈i/ρ)…”
Fokker–Planck model for computational studies of monatomic rarefied gas flows (2011, background): “For example, in the R13 moment equations, the evolution of mass density, velocity, molecular stresses and heat fluxes for the gas is solved (see Struchtrup 2005; Torrilhon & Struchtrup 2008).”
Phonon hydrodynamics and its applications in nanoscale heat transport (2015, unknown): “The small parameter ε usually denotes Kn number (the ratio of mean free path to the characteristic size of fluid system) in classical hydrodynamics [154,155].”