Linear stability analysis for various forms of one-dimensional burnett equations

The characteristic equations of one-dimensional original Burnett, conventional Burnett, augmented Burnett, BGK-Burnett and Woods equations are derived, linear stability analysis is made. The critical Knudsen number for these unstable equations is calculated. The results show that the critical Knudsen number for the conventional Burnett and Woods equations with material derivatives approximated by the Euler equations are about 2.455 and 0.907, respectively. When no approximation is made for the Burnett equations, the critical Knudsen numbers for original Burnett, augmented Burnett, BGK-Burnett and Woods