Globally Hyperbolic Moment Equations in Kinetic Gas Theory

Manuel Torrilhon
ETH Zürich

Moment equations as approximation of kinetic equations became a powerful tool to describe, for example, non-equilirbium gas dynamics. They come as systems of partial differential equations with a hyperbolic core that models the kinetic free flight and dissipative relaxation or diffusion for the collisional interaction. Unfortunately, all available moment equations are only locally hyperbolic and fail to compute strong non-linear, high speed processes due to unphysical elliptic behavior. The maximum entropy closure promises hyperbolicity formally, but the maximization has been shown to be ill-posed.
In this talk we present a new closure for moment equations that turns out to be hyperbolic for all physically relevant states. It is based on special statistics for the kinetic equation using Pearson-Type-IV distribution functions. This distribution generalizes the Maxwellian distribution to include anisotropies and skewness, yet allows for analytic expressions for all moments making the closure very simple. We will investigate different cases and compute regions of hyperbolicity and several Riemann problems as test cases.

Presentation (PDF File)

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