  We introduce a numerical solver for the spatially inhomogeneous Boltzmann
equation using the Burnett spectral method. The modelling and discretization of
the collision operator are based on the previous work [Z. Cai, Y. Fan, and Y.
Wang, Burnett spectral method for the spatially homogeneous Boltzmann equation,
arXiv:1810.07804], which is the hybridization of the BGK operator for higher
moments and the quadratic collision operator for lower moments. To ensure the
preservation of the equilibrium state, we introduce an additional term to the
discrete collision operator, which equals zero when the number of degrees of
freedom tends to infinity. Compared with the previous work [Z. Hu, Z. Cai, and
Y. Wang,Numerical simulation of microflows using Hermite spectral methods,
arXiv:1807.06236], the computational cost is reduced by one order. Numerical
experiments such as shock structure calculation and Fourier flows are carried
out to show the efficiency and accuracy of our numerical method.
