Lattice Boltzmann Simulation of Nonequilibrium Flows Using Spectral Multiple-Relaxation-Time Collision Model

Abstract

Prediction of nonequilibrium flows is critical to space flight. The present work demonstrates that the recently developed spectral multiple-relaxation-time (SMRT) lattice Boltzmann (LB) model is theoretically equivalent to Grad’s eigensystem [“Principles of the Kinetic Theory of Gases,” Thermodynamik der Gase/Thermodynamics of Gases, Springer–Verlag, Berlin, 1958, pp. 205–294], where the eigenfunctions obtained by tensor decomposition of the Hermite polynomials are also those of the linearized Boltzmann equation. Numerical results of shock structure simulation using the 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 is used, such as in the Shakhov model and lumped-sum relaxation of Hermite modes, non-negligible discrepancies start to occur as the 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 nonequilibrium flow simulation.