Applications of discontinuous Galerkin methods to the simulation of kinetic equations

Includes bibliographical references (pages 63-64)Numerical modeling of the behavior of gas flows over sharp leading edges of air vehicles are challenging because they require the solution of model kinetic equations. These equations lead to stiff problems in regimes transitional from continuum to free molecular, therefore the development of methods that are high order and high resolution receive a lot of interest. We develop an efficient algorithm for high-order, high-accuracy solutions to model kinetic equations of gas dynamics using multiple time stepping schemes and mesh refinement based on the discontinuous Galerkin (DG) approximation in both spatial and velocity variables. we apply this method to the simulation of normal shock wave problem and heat transfer problem to demonstrate the methods??? efficiently