Stability Analysis of Quadrature-Based Moment Methods for Kinetic Equations

In this paper, we give a systematic stability analysis of the quadrature-based moment method (QBMM) for the one-dimensional Boltzmann equation with BGK or Shakhov models. As reported in recent literature, the method has revealed its potential for modeling nonequilibrium flows, while a thorough theoretical analysis is largely missing but desirable. We show that the method can yield nonhyperbolic moment systems if the distribution function is...