A new class of accurate, meshfree hydrodynamic simulation methods
Abstract
We present two new Lagrangian methods for hydrodynamics, in a systematic comparison with movingmesh, smoothed particle hydrodynamics (SPH), and stationary (nonmoving) grid methods. The new methods are designed to simultaneously capture advantages of both SPH and gridbased/adaptive mesh refinement (AMR) schemes. They are based on a kernel discretization of the volume coupled to a highorder matrix gradient estimator and a Riemann solver acting over the volume `overlap'. We implement and test a parallel, secondorder version of the method with selfgravity and cosmological integration, in the code GIZMO:^{1} this maintains exact mass, energy and momentum conservation; exhibits superior angular momentum conservation compared to all other methods we study; does not require `artificial diffusion' terms; and allows the fluid elements to move with the flow, so resolution is automatically adaptive. We consider a large suite of test problems, and find that on all problems the new methods appear competitive with movingmesh schemes, with some advantages (particularly in angular momentum conservation), at the cost of enhanced noise. The new methods have many advantages versus SPH: proper convergence, good capturing of fluidmixing instabilities, dramatically reduced `particle noise' and numerical viscosity, more accurate subsonic flow evolution, and sharp shockcapturing. Advantages versus nonmoving meshes include: automatic adaptivity, dramatically reduced advection errors and numerical overmixing, velocityindependent errors, accurate coupling to gravity, good angular momentum conservation and elimination of `grid alignment' effects. We can, for example, follow hundreds of orbits of gaseous discs, while AMR and SPH methods break down in a few orbits. However, fixed meshes minimize `grid noise'. These differences are important for a range of astrophysical problems.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 June 2015
 DOI:
 10.1093/mnras/stv195
 arXiv:
 arXiv:1409.7395
 Bibcode:
 2015MNRAS.450...53H
 Keywords:

 hydrodynamics;
 instabilities;
 turbulence;
 methods: numerical;
 cosmology: theory;
 Astrophysics  Cosmology and Nongalactic Astrophysics;
 Astrophysics  Astrophysics of Galaxies;
 Astrophysics  Instrumentation and Methods for Astrophysics;
 Physics  Computational Physics;
 Physics  Fluid Dynamics
 EPrint:
 57 pages, 33 figures. MNRAS. A public version of the GIZMO code, user's guide, test problem setups, and movies are available at http://www.tapir.caltech.edu/~phopkins/Site/GIZMO.html