skip to main content

SciTech ConnectSciTech Connect

Title: NUMERICAL CONVERGENCE IN SMOOTHED PARTICLE HYDRODYNAMICS

We study the convergence properties of smoothed particle hydrodynamics (SPH) using numerical tests and simple analytic considerations. Our analysis shows that formal numerical convergence is possible in SPH only in the joint limit N → ∞, h → 0, and N{sub nb} → ∞, where N is the total number of particles, h is the smoothing length, and N{sub nb} is the number of neighbor particles within the smoothing volume used to compute smoothed estimates. Previous work has generally assumed that the conditions N → ∞ and h → 0 are sufficient to achieve convergence, while holding N{sub nb} fixed. We demonstrate that if N{sub nb} is held fixed as the resolution is increased, there will be a residual source of error that does not vanish as N → ∞ and h → 0. Formal numerical convergence in SPH is possible only if N{sub nb} is increased systematically as the resolution is improved. Using analytic arguments, we derive an optimal compromise scaling for N{sub nb} by requiring that this source of error balance that present in the smoothing procedure. For typical choices of the smoothing kernel, we find N{sub nb} ∝N {sup 0.5}. This means that if SPH is tomore » be used as a numerically convergent method, the required computational cost does not scale with particle number as O(N), but rather as O(N {sup 1} {sup +} {sup δ}), where δ ≈ 0.5, with a weak dependence on the form of the smoothing kernel.« less
Authors:
;  [1] ;  [2]
  1. Department of Astronomy and Astrophysics, The Pennsylvania State University, 525 Davey Lab, University Park, PA 16802 (United States)
  2. Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138 (United States)
Publication Date:
OSTI Identifier:
22364283
Resource Type:
Journal Article
Resource Relation:
Journal Name: Astrophysical Journal; Journal Volume: 800; Journal Issue: 1; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; COMPUTER CALCULATIONS; COMPUTERIZED SIMULATION; CONVERGENCE; HYDRODYNAMICS; KERNELS; RESOLUTION