Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: GIZMO: A New Class of Accurate, Mesh-Free Hydrodynamic Simulation
  Methods   We present two new Lagrangian methods for hydrodynamics, in a systematic
comparison with moving-mesh, SPH, and stationary (non-moving) grid methods. The
new methods are designed to simultaneously capture advantages of both
smoothed-particle hydrodynamics (SPH) and grid-based/adaptive mesh refinement
(AMR) schemes. They are based on a kernel discretization of the volume coupled
to a high-order matrix gradient estimator and a Riemann solver acting over the
volume 'overlap.' We implement and test a parallel, second-order version of the
method with self-gravity & cosmological integration, in the code GIZMO: 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 moving-mesh schemes, with some advantages (particularly in
angular momentum conservation), at the cost of enhanced noise. The new methods
have many advantages vs. SPH: proper convergence, good capturing of
fluid-mixing instabilities, dramatically reduced 'particle noise' & numerical
viscosity, more accurate sub-sonic flow evolution, & sharp shock-capturing.
Advantages vs. non-moving meshes include: automatic adaptivity, dramatically
reduced advection errors & numerical overmixing, velocity-independent 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 disks, 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.

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The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
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The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: stat
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The categories of this paper are: atom-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: gr-qc