Globally hyperbolic regularization to Grad's moment system
The Grad's moment method, as a kind of approximation to the Boltzmann equation, has been introduced more than sixty years ago. The method systematically derives a sequence of high order macroscopic hydrodynamic models, including for example the famous 13-moment system. However the basic method suffers from some drawbacks which limit its implementation, most notably its lack of hyperbolicity in some regions. It is well-know that the 13-moment system in 1D case is hyperbolic around the local equilibrium. We revealed amazingly that for 3D case the 13-moment system do NOT admit the local equilibrium as the interior point of its hyperbolicity region. Furthermore, a new theory was developed to regularize the Grad's moment system for arbitrary order to achieve global hyperbolicity. The regularized system is an elegant extension of Euler equations, with all its wave speeds and characteristic fields fully clarified, and formally preserving the spectral convergence of Grad's expansion.