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Numerical Properties of High Order Discrete Velocity Solutions to the BGK Kinetic Equation
 

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 Runge-Kutta discretizations in
the temporal variable. The method is implemented for the one-dimensional
Bhatnagar-Gross-Krook 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,
Runge-Kutta methods, Transient gas flows
2000 MSC: 76M10, 76P05, 65M60
1. Introduction
High resolution simulations of gas flows in the non-continuum regime are
emerging as an important area of practical interest. Applications of non-continuum

  

Source: Alekseenko, Alexander - Department of Mathematics, California State University, Northridge

 

Collections: Physics