Simulation of incompressible fluids is widely used for studies of fluid mechanics and for visual effects in computer graphics. One major challenge is to capture dynamics of thin vortices in finite grid resolution. We describe a new approach to the simulation of incompressible fluids in 3D. In it, the fluid state is represented by complex-valued wave functions evolving under the Schrödinger equation subject to incompressible constraints. We call it incompressible Schrödinger equation. We show that the underlying dynamical system is Hamiltonian corresponding to a modified Euler equation with a magnetic Landau-Lifshitz term. The latter ensures that dynamics due to thin vortical structures are faithfully reproduced. This enables robust simulation of intricate phenomena such as vortical wakes and interacting vortex filaments, even on modestly sized computation grid. The resulting algorithm is simple, unconditionally stable, and efficient. This talk represents joint work with Felix Knöppel, Ulrich Pinkall, Peter Schröder and
Steffen Weißmann.