Abstract：

In this talk, I will present the stability analysis of the hyperbolic shallow water moment system and the quadrature-based moment closure systems. The former describes shallow flows for complex velocity profiles which vary in vertical direction and the models can be seen as extensions of the standard shallow water equations. The latter, on the other hand, generates high-order hydrodynamic equations for the rarefied flow from the Boltzmann-type equation. Equilibrium stability is an important property of balance laws that determines the linear stability of solutions in the vicinity of equilibrium manifolds, and it is seen as a necessary condition for stable numerical solutions. I will show the results of our analysis, with emphasis on the implication on the practical numerical performance.