An asymptotically preserving scheme for nonlinear Schrodinger equation in the semiclassical limit. (arXiv:1002.1627v1 [math.NA])

An asymptotically preserving scheme for nonlinear Schrodinger equation in the semiclassical limit. (arXiv:1002.1627v1 [math.NA]): "

We study numerically the semiclassical limit for the nonlinear Schrodinger
equation thanks to a modification of the Madelung transform due to E.Grenier.
This approach is naturally asymptotically preserving. Even if the mesh size and
the time step do not depend on the Planck constant, we recover the position and
current densities in the semiclassical limit, with a numerical rate of
convergence in accordance with the theoretical results, before shocks appear in
the limiting Euler equation. By using simple projections, the mass and the
momentum of the solution are well preserved by the numerical scheme, while the
variation of the energy is not negligible numerically.

"