  To close the moment model deduced from kinetic equations, the canonical
approach is to provide an approximation to the flux function not able to be
depicted by the moments in the reduced model. In this paper, we propose a brand
new closure approach with remarkable advantages than the canonical approach.
Instead of approximating the flux function, the new approach close the moment
model by approximating the flux gradient. Precisely, we approximate the space
derivative of the distribution function by an ansatz which is a weighted
polynomial, and the derivative of the closing flux is computed by taking the
moments of the ansatz. Consequently, the method provides us an improved
framework to derive globally hyperbolic moment models, which preserve all those
conservative variables in the low order moments. It is shown that the
linearized system at the weight function, which is often the local equilibrium,
of the moment model deduced by our new approach is automatically coincided with
the system deduced from the classical perturbation theory, which can not be
satisfied by previous hyperbolic regularization framework. Taking the Boltzmann
equation as example, the linearlization of the moment model gives the correct
Navier-Stokes-Fourier law same as that the Chapman-Enskog expansion gives. Most
existing globally hyperbolic moment models are re-produced by our new approach,
and several new models are proposed based on this framework.
