 
Summary: The Application of Discontinuous Galerkin Space and Velocity
Discretization to Model Kinetic Equations
Alexander Alekseenko1
, Natalia Gimelshein2
and Sergey Gimelshein2
1
Department of Mathematics, California State University Northridge, Northridge,
California 91330, USA
2
ERC, Inc, Edwards AFB, California 93524, USA
Abstract. An approach based on a discontinuous Galerkin discretiza
tion is proposed for the BhatnagarGrossKrook model kinetic equa
tion. This approach allows for a high order polynomial approximation
of molecular velocity distribution function both in spatial and velocity
variables. It is applied to model normal shock wave and heat transfer
problems. Convergence of solutions with respect to the number of spatial
cells and velocity bins is studied, with the degree of polynomial approxi
mation ranging from zero to four in the physical space variable and from
zero to eight in the velocity variable. This approach is found to conserve
mass, momentum and energy when high degree polynomial approxima
