  We present a class of arbitrarily high order fully explicit kinetic numerical
methods in compressible fluid dynamics, both in time and space, which include
the relaxation schemes by S. Jin and Z. Xin. These methods can use CFL number
larger or equal to unity on regular Cartesian meshes for multi-dimensional
case. These kinetic models depend on a small parameter that can be seen as a
"Knudsen" number. The method is asymptotic preserving in this Knudsen number.
Also, the computational costs of the method are of the same order of a fully
explicit scheme. This work is the extension of Abgrall et al. (2022)
\cite{Abgrall} to multi-dimensional systems.
  We have assessed our method on several problems for two dimensional scalar
problems and Euler equations and the scheme has proven to be robust and to
achieve the theoretically predicted high order of accuracy on smooth solutions.

Numerical Analysis;Numerical Analysis