  In this paper, we prove the compressible Euler limit from the Boltzmann
equation with hard sphere collisional kernel and complete diffusive boundary
condition in half-space by employing the Hilbert expansion which includes
interior and Knudsen layers. This rigorously justifies the corresponding formal
analysis in Sone's book \cite{Sone-2007-Book} in the context of short time
smooth solutions, and also generalizes the classic Caflisch's result
\cite{Caflish-1980-CPAM} to initial-boundary problem case.
