  We use the Burnett spectral method to solve the Boltzmann equation whose
collision term is modeled by separate treatments for the low-frequency part and
high-frequency part of the solution. For the low-frequency part representing
the sketch of the distribution function, the binary collision is applied, while
for the high-frequency part representing the finer details, the BGK
approximation is applied. The parameter controlling the ratio of the
high-frequency part and the low-frequency part is selected adaptively on every
grid cell at every time step. This self-adaptation is based on an error
indicator describing the difference between the model collision term and the
original binary collision term. The indicator is derived by controlling the
quadratic terms in the modeling error with linear operators. Our numerical
experiments show that such an error indicator is effective and computationally
affordable.
