A Stable Finite-Volume Method for Scalar-Field Dark Matter. (arXiv:1811.05583v1 [astro-ph.CO])
<a href="http://arxiv.org/find/astro-ph/1/au:+Hopkins_P/0/1/0/all/0/1">Philip F. Hopkins</a> (Caltech)

We describe and test a new numerical method to solve the Schrodinger equation
in self-gravitating systems, e.g. Bose-Einstein condensates or
‘fuzzy’/ultra-light dark matter. The method is a finite-volume Godunov scheme
with stable, higher-order accurate gradient estimation, based on a
generalization of recent mesh-free finite-mass Godunov methods. It couples
easily to particle-based N-body gravity solvers (with or without other fluids,
e.g. baryons), manifestly conserves momentum and energy, is numerically stable,
and computationally efficient. We consider a variety of test problems and
demonstrate that it can accurately recover exact solutions and remains stable
even in noisy, poorly-resolved systems, with dramatically reduced noise
compared to other proposed implementations. This is non-trivial because the
‘quantum pressure’ is neither isotropic nor positive-definite and depends on
higher-order gradients of the density field. We implement and test the method
in the code GIZMO.

We describe and test a new numerical method to solve the Schrodinger equation
in self-gravitating systems, e.g. Bose-Einstein condensates or
‘fuzzy’/ultra-light dark matter. The method is a finite-volume Godunov scheme
with stable, higher-order accurate gradient estimation, based on a
generalization of recent mesh-free finite-mass Godunov methods. It couples
easily to particle-based N-body gravity solvers (with or without other fluids,
e.g. baryons), manifestly conserves momentum and energy, is numerically stable,
and computationally efficient. We consider a variety of test problems and
demonstrate that it can accurately recover exact solutions and remains stable
even in noisy, poorly-resolved systems, with dramatically reduced noise
compared to other proposed implementations. This is non-trivial because the
‘quantum pressure’ is neither isotropic nor positive-definite and depends on
higher-order gradients of the density field. We implement and test the method
in the code GIZMO.

http://arxiv.org/icons/sfx.gif