  A type of discrete Boltzmann model for simulating shallow water flows is
derived by using the Hermite expansion approach. Through analytical analysis,
we study the impact of truncating distribution function and discretizing
particle velocity space. It is found that the convergence behavior of expansion
is nontrivial while the conservation laws are naturally satisfied. Moreover,
the balance of source terms and flux terms for steady solutions is not
sacrificed. Further numerical validations show that the capability of
simulating supercritical flows is enhanced by employing higher order expansion
and quadrature.
