 
Summary: Numerical Properties of High Order Discrete Velocity
Solutions to the BGK Kinetic Equation
A.M. Alekseenkoa
aDepartment of Mathematics, California State University, Nortrhidge, CA 91330, USA
Abstract
A high order numerical method for the solution of model kinetic equations is
proposed. The new method employs discontinuous Galerkin (DG) discretiza
tions in the spatial and velocity variables and RungeKutta discretizations in
the temporal variable. The method is implemented for the onedimensional
BhatnagarGrossKrook equation. Convergence of the numerical solution and
accuracy of the evaluation of macroparameters is studied for different orders
of velocity discretization. Synthetic model problems are proposed and imple
mented to test accuracy of discretizations in the free molecular regime. The
method is applied to the solution of the normal shock wave problem.
Key words: Kinetic equations, Discontinuous Galerkin methods,
RungeKutta methods, Transient gas flows
2000 MSC: 76M10, 76P05, 65M60
1. Introduction
High resolution simulations of gas flows in the noncontinuum regime are
emerging as an important area of practical interest. Applications of noncontinuum
