A new class of accurate, mesh-free hydrodynamic simulation methods
Abstract
We present two new Lagrangian methods for hydrodynamics, in a systematic comparison with moving-mesh, smoothed particle hydrodynamics (SPH), and stationary (non-moving) grid methods. The new methods are designed to simultaneously capture advantages of both 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 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 moving-mesh 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 fluid-mixing instabilities, dramatically reduced `particle noise' and numerical viscosity, more accurate sub-sonic flow evolution, and sharp shock-capturing. Advantages versus non-moving meshes include: automatic adaptivity, dramatically reduced advection errors and 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 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
- E-Print:
- 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