  In this paper, we propose an efficient, high order accurate and
asymptotic-preserving (AP) semi-Lagrangian (SL) method for the BGK model with
constant or spatially dependent Knudsen number. The spatial discretization is
performed by a mass conservative nodal discontinuous Galerkin (NDG) method,
while the temporal discretization of the stiff relaxation term is realized by
stiffly accurate diagonally implicit Runge-Kutta (DIRK) methods along
characteristics. Extra order conditions are enforced for asymptotic accuracy
(AA) property of DIRK methods when they are coupled with a semi-Lagrangian
algorithm in solving the BGK model. A local maximum principle preserving (LMPP)
limiter is added to control numerical oscillations in the transport step.
Thanks to the SL and implicit nature of time discretization, the time stepping
constraint is relaxed and it is much larger than that from an Eulerian
framework with explicit treatment of the source term. Extensive numerical tests
are presented to verify the high order AA, efficiency and shock capturing
properties of the proposed schemes.
