| 講演要旨： |
I will review several recent methods for kinetic problems where the mean free path has different orders of magnitude.
In particular, I will present
- asymptotic-preserving methods: which solve the kinetic problems with numerical resolution at hydrodynamic scales without using the hydrodynamic equations
- domain decomposition methods: we provide interface conditions that allow us to couple a kinetic equation with a (hydrodynamic) diffusion equation for numerical computation without using iterations at each time step
- Moment closure and Burnett equations: we will provide a relaxation regularization to the Burnett equations. The new moment system is linearly hyperbolic and stable, and matched the solution of the Boltzmann equation to the Burnett order.
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