Derivation of regularized Grad's moment system from kinetic equations: modes, ghosts and non-Markov fluxes

作者：Karlin Ilya^*

来源：Philosophical Transactions of the Royal Society A-Mathematical Physical and Engineering Sciences, 2018, 376(2118): 20170230.

DOI：10.1098/rsta.2017.0230

• Boltzmann equation
• moment methods
• invariant manifold

Derivation of the dynamic correction to Grad's moment system from kinetic equations (regularized Grad's 13 moment system, or R13) is revisited. The R13 distribution function is found as a superposition of eight modes. Three primary modes, known from the previous derivation (Karlin et al. 1998 Phys. Rev. E 57, 1668-1672. (doi:10.1103/PhysRevE.57.1668)), are extended into the nonlinear parameter domain. Three essentially nonlinear modes are identified, and two ghostmodes which do not contribute to the R13 fluxes are revealed. The eight-mode structure of the R13 distribution function implies partition of R13 fluxes into two types of contributions: dissipative fluxes (both linear and nonlinear) and nonlinear streamline convective fluxes. Physical interpretation of the latter non-dissipative and non-local in time effect is discussed. A non-perturbative R13-type solution is demonstrated for a simple Lorentz scattering kinetic model. The results of this study clarify the intrinsic structure of the R13 system.

• 出版日期2018-4-28