Young Researchers Workshop: Kinetic theory with applications in physical sciences

Moment methods and adaptive spectral methods in the gas kinetic theory

Zhenning Cai

Duke University
[SLIDES]

We regularize Grad's moment method by a hyperbolicity fix to obtain global hyperbolicity. By investigating the numerical scheme of this new method, the moment method is naturally linked to the adaptive spectral method for the Boltzmann equation. From this point of view, the hyperbolic moment method is further improved to get the convergence for a wider range of distribution functions. Difficulties in the new type of adaptive spectral method will be presented and some possible solutions and extensions will be discussed.