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Prediction of non-equilibrium flows is critical to space flight. In thepresent work we demonstrate that the recently developed spectralmultiple-relaxation-time (SMRT) lattice Boltzmann (LB) model is theoreticallyequivalent to Grad's eigen-system [Grad, H., In Thermodynamics of Gases (1958)]where the eigen-functions obtained by tensor decomposition of the Hermitepolynomials are also those of the linearized Boltzmann equation. Numericalresults of shock structure simulation using Maxwell molecular model agree verywell with those of a high-resolution fast spectral method code up to Mach 7provided that the relaxation times of the irreducible tensor components matchtheir theoretical values. If a reduced set of relaxation times are used such asin the Shakhov model and lumped-sum relaxation of Hermite modes, non-negligiblediscrepancies starts to occur as Mach number is raised, indicating thenecessity of the fine-grained relaxation model. Together with the provenadvantages of LB, the LB-SMRT scheme offers a competitive alternative fornon-equilibrium flow simulation.

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