  We consider an anisotropic model case for a strictly convex domain of
dimension $d\geq 2$ with smoothboundary and we describe dispersion forthe
semi-classical Schr{\"o}dinger equation with Dirichlet boundary condition. More
specifically, we obtain the following fixed time decay rate for the linear
semi-classical flow : a loss of $(\frac ht)^{1/4}$ occurs with respect to the
boundary less case due to repeated swallowtail type singularities, and is
proven optimal. Corresponding Strichartz estimates allow to solve the cubic
nonlinear Sch\"odinger equation on such a 3D model convex domain, hence
matching known results on generic compact boundaryless manifolds.
