A new approach to simulating collisionless dark matter fluids
  Recently, we have shown how current cosmological N-body codes already follow
the fine grained phase-space information of the dark matter fluid. Using a
tetrahedral tesselation of the three-dimensional manifold that describes
perfectly cold fluids in six-dimensional phase space, the phase-space
distribution function can be followed throughout the simulation. This allows
one to project the distribution function into configuration space to obtain
highly accurate densities, velocities, and velocity dispersions. Here, we
exploit this technique to show first steps on how to devise an improved
particle-mesh technique. At its heart, the new method thus relies on a
piecewise linear approximation of the phase space distribution function rather
than the usual particle discretisation. We use pseudo-particles that
approximate the masses of the tetrahedral cells up to quadrupolar order as the
locations for cloud-in-cell (CIC) deposit instead of the particle locations
themselves as in standard CIC deposit. We demonstrate that this modification
already gives much improved stability and more accurate dynamics of the
collisionless dark matter fluid at high force and low mass resolution. We
demonstrate the validity and advantages of this method with various test
problems as well as hot/warm-dark matter simulations which have been known to
exhibit artificial fragmentation. This completely unphysical behaviour is much
reduced in the new approach. The current limitations of our approach are
discussed in detail and future improvements are outlined.
