  In this paper we study the geometry of the special fiber of Pappas-Rapoport
models of Shimura varieties in the Hilbert case. More precisely we prove that
the stratification induced by the Hodge polygon is a good stratification, which
is false in the Hilbert-Siegel case for $g\geq 2$. Then we use known results on
the convolution product of affine Grassmannians to describe the dimension of
the strata and obtain that the forgetting morphism to the Kottwitz PEL model is
flat in restriction to Hodge strata.
