Lattice Boltzmann simulation of non-equilibrium flows using spectral multiple-relaxation-time collision model

Abstract

Prediction of non-equilibrium flows is critical to space flight. In the present work we demonstrate that the recently developed spectral multiple-relaxation-time (SMRT) lattice Boltzmann (LB) model is theoretically equivalent to Grad's eigen-system [Grad, H., In Thermodynamics of Gases (1958)] where the eigen-functions obtained by tensor decomposition of the Hermite polynomials are also those of the linearized Boltzmann equation. Numerical results of shock structure simulation using Maxwell molecular model agree very well with those of a high-resolution fast spectral method code up to Mach 7 provided that the relaxation times of the irreducible tensor components match their theoretical values. If a reduced set of relaxation times are used such as in the Shakhov model and lumped-sum relaxation of Hermite modes, non-negligible discrepancies starts to occur as Mach number is raised, indicating the necessity of the fine-grained relaxation model. Together with the proven advantages of LB, the LB-SMRT scheme offers a competitive alternative for non-equilibrium flow simulation.