  Most of numerical methods for deterministic simulations of rarefied gas flows
use the discrete velocity (or discrete ordinate) approximation. In this
approach, the kinetic equation is approximated with a global velocity grid. The
grid must be large and fine enough to capture all the distribution functions,
which is very expensive for high speed flows (like in hypersonic aerodynamics).
In this article, we propose to use instead different velocity grids that are
local in time and space: these grids dynamically adapt to the width of the
distribution functions. The advantages and drawbacks of the method are
illustrated in several 1D test cases.
